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Factoring Trinomials I
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Factoring Trinomials I
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers.
------=_NextPart_01C8FD9E.94234A60 Content-Location: file:///C:/A0C234E9/2factoringtrinomialI_files/slide0095.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Factoring Trinomials I
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
------=_NextPart_01C8FD9E.94234A60 Content-Location: file:///C:/A0C234E9/2factoringtrinomialI_files/slide0096.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Factoring Trinomials I
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible,
------=_NextPart_01C8FD9E.94234A60 Content-Location: file:///C:/A0C234E9/2factoringtrinomialI_files/slide0097.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Factoring Trinomials I
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
------=_NextPart_01C8FD9E.94234A60 Content-Location: file:///C:/A0C234E9/2factoringtrinomialI_files/slide0098.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Review on Factoring
Factoring Trinomials I
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
To factor= x2 + bx + c, we note hat <= /div>
if (x + <= /span>u)(x + v)<= /div>
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
To factor= x2 + bx + c, we note hat <= /div>
if (x + <= /span>u)(x + v)
=3D x2 + <= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>ux = + vx + uv <= /div>
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
To factor= x2 + bx + c, we note hat <= /div>
if (x + <= /span>u)(x + v)
=3D x2 + <= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>ux = + vx + uv
=3D x2 + (u + v)x + uv
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
To factor= x2 + bx + c, we note hat <= /div>
if (x + <= /span>u)(x + v)
=3D x2 + <= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>ux = + vx + uv
=3D x2 + (u + v)x + uv
=3D x2 + bx + c,
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
To factor= x2 + bx + c, we note hat <= /div>
if (x + <= /span>u)(x + v)
=3D x2 + <= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>ux = + vx + uv
=3D x2 + (u + v)x + uv
=3D x2 + bx + c,
we need t= o have u and v where uv =3D c, =
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
To factor= x2 + bx + c, we note hat <= /div>
if (x + <= /span>u)(x + v)
=3D x2 + <= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>ux = + vx + uv
=3D x2 + (u + v)x + uv
=3D x2 + bx + c,
we need t= o have u and v where uv =3D c, and u + v =3D b. <= /div>
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
To factor= x2 + bx + c, we note hat <= /div>
if (x + <= /span>u)(x + v)
=3D x2 + <= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>ux = + vx + uv
=3D x2 + (u + v)x + uv
=3D x2 + bx + c,
we need t= o have u and v where uv =3D c, and u + v =3D b. If this = can’= ;t be done, then the trinomial is prime (not factorable).
Trinomials (three-term) are polynomials of the form
ax= 2 + bx + c where a, b, and c are numbers. The product of two binom= ials is a trinomials:
(#x + #)(#x + #) à ax2 + bx + c
Hence, to= factor a trinomial, we write the trinomial as a product of two binomia= ls, if possible, that is:
          = ;   ax2 + bx + c à (#x + #)(#x + #)
We start = with the case where a =3D 1, or trinomials
of the fo= rm x2 + bx + c.
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5.
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. =
Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3) 
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. =
Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5,
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
b. Factor x2 – 5x + 6
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v where uv =3D 6
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 = – 5x + 6, so we need u and v where uv= =3D 6 and u + v =3D –5.
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v= where uv =3D 6 and u + v =3D –5.
Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and –2 – 3 =3D –5,
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v= where uv =3D 6 and u + v =3D –5. Since 6 = =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and –2 – 3 =3D –5, so x2 – 5x + 6 =3D (x – 2)(x= – 3).
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
c.  Factor x2 + 5x – 6
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v= where uv =3D 6 and u + v =3D –5. Since 6 = =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and –2 – 3 =3D –5, so x2 – 5x + 6 =3D (x – 2)(x= – 3).
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
c.  Factor x2 + 5x – 6
We want (x + u)(x + v) =3D x2 = + 5x – 6, so we need uv =3D –6 =
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v= where uv =3D 6 and u + v =3D –5. Since 6 = =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and –2 – 3 =3D –5, so x2 – 5x + 6 =3D (x – 2)(x= – 3).
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
c.  Factor x2 + 5x – 6
We want (x + u)(x + v) =3D x2 = + 5x – 6, so we need uv =3D –6 and u + v = =3D 5.
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v= where uv =3D 6 and u + v =3D –5. Since 6 = =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and –2 – 3 =3D –5, so x2 – 5x + 6 =3D (x – 2)(x= – 3).
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
c.  Factor x2 + 5x – 6
We want (x + u)(x + v) =3D x2 = + 5x – 6, so we need uv =3D –6 and u + v = =3D 5.
Since -6 =3D (–1)(6) =3D (1)(–6) =3D (–2)(3) =3D(2)(–3) = and –1 + 6 =3D 5,
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v= where uv =3D 6 and u + v =3D –5. Since 6 = =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and –2 – 3 =3D –5, so x2 – 5x + 6 =3D (x – 2)(x= – 3).
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Factoring Trinomials I
Example A. 
a. Factor x2 + 5x + 6
We want (x + u)(x + v) =3D x2 = + 5x + 6, so we need u and v where uv =3D 6 and u + v =3D 5. = Since 6 =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and 2 + 3 =3D 5, so x2 + 5x + 6 =3D (x + 2)(x + 3).
c.  Factor x2 + 5x – 6
We want (x + u)(x + v) =3D x2 = + 5x – 6, so we need uv =3D –6 and u + v = =3D 5. Since -6 =3D (–1)(6) =3D (1)(–6) = =3D (–2)(3) =3D(2)(–3) and –1 + 6 =3D 5, so x2 + 5x – 6 =3D (x – 1)(x= + 6).   
b. Factor x2 – 5x + 6
We want (x + u)(x + v) =3D x2 – 5x + 6, so we need u and v= where uv =3D 6 and u + v =3D –5. Since 6 = =3D (1)(6) =3D (2)(3) =3D (-1)(-6) =3D (-2)(-3)  and –2 – 3 =3D –5, so x2 – 5x + 6 =3D (x – 2)(x= – 3).
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Factoring Trinomials I
Observations About Signs
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Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
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Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
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Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
    In particular,
     if b= is also positive, then both are positive.
    
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Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
    In particular,
     if b= is also positive, then both are positive.
       
    From the examples abo= ve
    x2 = + 5x = + 6 =3D (x= + 2)(x + 3) <= /span>
   
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Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
    In particular,
     if b= is also positive, then both are positive.
     if b= is negat= ive, then both are negative.  = ;
    From the examples abo= ve
    x2 = + 5x + 6 =3D (x= + 2)(x + 3)
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{
Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
    In particular,
     if b= is also positive, then both are positive.
     if b= is negat= ive, then both are negative.  = ;
    From the examples abo= ve
    x2 = + 5x = + 6 =3D (x= + 2)(x + 3) <= /span>
    x2 = – 5x + 6 =3D (x= – 2)(x – 3)
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{
Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
    In particular,
     if b= is also positive, then both are positive.
     if b= is negat= ive, then both are negative.  = ;
    From the examples abo= ve
    x2 = + 5x + 6 =3D (x= + 2)(x + 3) <= /span>
    x2 = – 5x + 6 =3D (x= – 2)(x – 3) <= /span>
2. If c is negat= ive, then u and v have opposite signs.
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{
Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
    In particular,
     if b= is also positive, then both are positive.
     if b= is negat= ive, then both are negative.  = ;
    From the examples abo= ve
    x2 = + 5x + 6 =3D (x= + 2)(x + 3) <= /span>
    x2 = – 5x + 6 =3D (x= – 2)(x – 3) <= /span>
2. If c is negat= ive, then u and v have opposite signs. The       = 3;
    one with larger absol= ute value has the same sign as b.
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{
Factoring Trinomials I
Observ= ations About Signs
Given tha= t x2 + b= x + c =3D (x += u)(x + v) so that uv =3D c,
we observ= e the following.
1. If c is posit= ive, then u and v have same sign.
    In particular,
     if b= is also positive, then both are positive.
     if b= is negat= ive, then both are negative.  = ;
    From the examples abo= ve
    x2 = + 5x + 6 =3D (x= + 2)(x + 3) <= /span>
    x2 = – 5x + 6 =3D (x= – 2)(x – 3) <= /span>
2. If c is negat= ive, then u and v have opposite signs. The       = 3;
    one with larger absol= ute value has the same sign as b.
    Fromd the example above
    x2 = – 5x – 6 =3D (x – 6)(x + 1)    
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12,
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4.
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4. Since -12 =3D (-1)(12) =3D (-2)(6) =3D (-3)(4)…
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4. Since -12 =3D (-1)(12) =3D (-2)(6) =3D (-3)(4)…
They must be –2 and 6
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4. Since -12 =3D (-1)(12) =3D (-2)(6) =3D (-3)(4)…
They must be –2 and 6 hence x2 = + 4x – 12 =3D (x – 2)(x + 6).
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4. Since -12 =3D (-1)(12) =3D (-2)(6) =3D (-3)(4)…
They must be –2 and 6 hence x2 = + 4x – 12 =3D (x – 2)(x + 6).
b.  Factor x2 – 8x – 12
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4. Since -12 =3D (-1)(12) =3D (-2)(6) =3D (-3)(4)…
They must be –2 and 6 hence x2 = + 4x – 12 =3D (x – 2)(x + 6).
b.  Factor x2 – 8x – 12 =
We need u and v such that uv =3D –12, u + v =3D –8 with
u and v having opposite signs.
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4. Since -12 =3D (-1)(12) =3D (-2)(6) =3D (-3)(4)…
They must be –2 and 6 hence x2 = + 4x – 12 =3D (x – 2)(x + 6).
b.  Factor x2 – 8x – 12 =
We need u and v such that uv =3D –12, u + v =3D –8 with
u and v having opposite signs. This is impossible.
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Factoring Trinomials I
Example B.
 
a. Factor x2 + 4x – 12
We need u and v having opposite signs such that uv =3D –12, u + v =3D +4. Since -12 =3D (-1)(12) =3D (-2)(6) =3D (-3)(4)…
They must be –2 and 6 hence x2 = + 4x – 12 =3D (x – 2)(x + 6).
b.  Factor x2 – 8x – 12 =
We need u and v such that uv =3D –12, u + v =3D –8 with
u and v having opposite signs. This is impossible.
Hence x2 – 8x – 12 is prime.
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document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) setTimeout("parent.GoToNextSld()",sld.mAdvDelay) } function GetObj(id) { if(g_supportsPPTHTML) return document.all(id); else return document.getElementById(id); } function SldHasTrans() { return SlideObj.style.filter !=3D ""; } function GetSldId()=20 { var regExp =3D /file:\/\/\//i var pos =3D location.href.search(regExp) if (MHTMLPrefix !=3D "" && pos !=3D -1) sId =3D location.href.substring(pos) else { sId =3D RemoveFilePrefixFromHref(location.href); var regExp =3D /\// var fixedHref =3D sId var pos =3D -1 =09 pos =3D fixedHref.search(regExp) while (pos !=3D -1) { fixedHref =3D fixedHref.replace(regExp, "\\") pos =3D fixedHref.search(regExp) } =09 if (g_fBaseHyperlink =3D=3D true) sId =3D "file:///" + fixedHref; else sId =3D fixedHref.substring(fixedHref.lastIndexOf('\\') + 1) } =09 return sId } function HideMenu() { if( frames["PPTSld"] && PPTSld.document.all.item("ctx= tmenu") && PPTSld.ctxtmenu.style.display!=3D"none" ) { PPTSld.ctxtmenu.styl= e.display=3D'none'; return true } return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } } function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && !parent.IsFramesMode() ) || (event && (event.keyCode=3D=3D32) ) ) parent.GoToNextSld(); } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D49, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0038.htm",1,-1,1),new hrefList(= "slide0094.htm",1,-1,1),new hrefList("slide0095.htm",1,-1,1),new hrefList("= slide0096.htm",1,-1,1),new hrefList("slide0097.htm",1,-1,1),new hrefList("s= lide0098.htm",1,-1,1),new hrefList("slide0099.htm",1,-1,1),new hrefList("sl= ide0100.htm",1,-1,1),new hrefList("slide0101.htm",1,-1,1),new hrefList("sli= de0102.htm",1,-1,1),new hrefList("slide0103.htm",1,-1,1),new hrefList("slid= e0104.htm",1,-1,1),new hrefList("slide0105.htm",1,-1,1),new hrefList("slide= 0049.htm",1,-1,1),new hrefList("slide0108.htm",1,-1,1),new hrefList("slide0= 109.htm",1,-1,1),new hrefList("slide0110.htm",1,-1,1),new hrefList("slide01= 11.htm",1,-1,1),new hrefList("slide0112.htm",1,-1,1),new hrefList("slide010= 6.htm",1,-1,1),new hrefList("slide0113.htm",1,-1,1),new hrefList("slide0114= .htm",1,-1,1),new hrefList("slide0115.htm",1,-1,1),new hrefList("slide0107.= htm",1,-1,1),new hrefList("slide0116.htm",1,-1,1),new hrefList("slide0117.h= tm",1,-1,1),new hrefList("slide0118.htm",1,-1,1),new hrefList("slide0119.ht= m",1,-1,1),new hrefList("slide0120.htm",1,-1,1),new hrefList("slide0093.htm= ",1,-1,1),new hrefList("slide0121.htm",1,-1,1),new hrefList("slide0122.htm"= ,1,-1,1),new hrefList("slide0123.htm",1,-1,1),new hrefList("slide0124.htm",= 1,-1,1),new hrefList("slide0125.htm",1,-1,1),new hrefList("slide0126.htm",1= ,-1,1),new hrefList("slide0127.htm",1,-1,1),new hrefList("slide0128.htm",1,= -1,1),new hrefList("slide0129.htm",1,-1,1),new hrefList("slide0082.htm",1,-= 1,1),new hrefList("slide0130.htm",1,-1,1),new hrefList("slide0131.htm",1,-1= ,1),new hrefList("slide0132.htm",1,-1,1),new hrefList("slide0133.htm",1,-1,= 1),new hrefList("slide0134.htm",1,-1,1),new hrefList("slide0135.htm",1,-1,1= ),new hrefList("slide0136.htm",1,-1,1),new hrefList("slide0137.htm",1,-1,1)= ,new hrefList("slide0138.htm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('


' + ENDSHOW_MESG + '

') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwBorder"].SetInactive =3D _BSetI_Border; gBtnArr["nb_sldshwText"] =3D new TxtBtn( "nb_sldshw","nb_sldshwText",parent= .FullScreen,null ) gBtnArr["nb_sldshwText"].SetActive =3D _BSetA_Border; gBtnArr["nb_sldshwText"].SetInactive =3D _BSetI_Border; gBtnArr["nb_voice"] =3D gBtnArr["nb_voiceBorder"] =3D new ImgBtn( "nb_voice= ","nb_voiceBorder",18,parent.ToggleVNarration ) gBtnArr["nb_otlTxtBorder"] =3D gBtnArr["nb_otlTxt"]=3D new ImgBtn( "nb_otlT= xt","nb_otlTxtBorder",23,parent.ToggleOtlText ) gBtnArr["nb_ntsBorder"].m_flagId=3D "nb_nts" gBtnArr["nb_ntsBorder"].SetFlag =3D NtsBtnSetFlag gBtnArr["nb_otlTxt"].ChangeIcon=3D GetOtlTxtState /********************************************* Context menu implementation _CM() is the function that's hooked up to the oncontextmenu event. Once we're asked to show the menu, we first build it by creating DIVs on-the-fly. Then we position it=20 within the screen area so it doesn't get clipped. Creating the DIVs using createElement() means we don't have to write out any extra HTML into the slide HTML files. **********************************************/ var sNext=3D"Next",sPrev=3D"Previous",sEnd=3D"End Show",sFont=3D"Arial",sAr= row=3D"Arrow",sFreeform=3D"Freeform",sRect=3D"Rectangle",sOval=3D"Oval" function ShowMenu() { BuildMenu(); var doc=3DPPTSld.document.body,x=3DPPTSld.event.clientX+doc.scrollLeft,y= =3DPPTSld.event.clientY+doc.scrollTop m =3D PPTSld.document.all.item("ctxtmenu") m.style.pixelLeft=3Dx if( (x+m.scrollWidth > doc.clientWidth)&&(x-m.scrollWidth > 0) ) m.style.pixelLeft=3Dx-m.scrollWidth m.style.pixelTop=3Dy if( (y+m.scrollHeight > doc.clientHeight)&&(y-m.scrollHeight > 0) ) m.style.pixelTop=3Dy-m.scrollHeight m.style.display=3D"" } function _CM() { if( !parent.IsFullScrMode() ) return; if(!PPTSld.event.ctrlKey) { ShowMenu() return false } else HideMenu() } function BuildMenu() { if( PPTSld.document.all.item("ctxtmenu") ) return var mObj=3DCreateItem( PPTSld.document.body ) mObj.id=3D"ctxtmenu" mObj.style.visibility=3D"hidden" var s=3DmObj.style s.position=3D"absolute" s.cursor=3D"default" s.width=3D"120px" SetCMBorder(mObj,"menu","black") var iObj=3DCreateItem( mObj ) SetCMBorder( iObj, "threedhighlight","threedshadow" ) iObj.style.padding=3D2 CreateMenuItem( iObj,sNext,M_GoNextSld,M_True ) CreateMenuItem( iObj,sPrev,M_GoPrevSld,M_HasPrevSld ) =09 CreateSeparator( iObj ) CreateMenuItem( iObj,sEnd,M_End,M_True ) mObj.style.visibility=3D"visible" } function Cancel() { window.event.cancelBubble=3Dtrue; window.event.returnVa= lue=3Dfalse } function Highlight() { ChangeClr("activecaption","threedhighlight") } function Deselect() { ChangeClr("threedface","menutext") } function Perform() { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) e.Action() else PPTSld.event.cancelBubble=3Dtrue } function ChangeClr( bg,clr ) { e=3DPPTSld.event.srcElement if( e.type=3D=3D"menuitem" && e.IsActive() ) { e.style.backgroundColor=3Dbg e.style.color=3Dclr } } function M_HasPrevSld() { return( parent.HasPrevSld() ) } function M_GoNextSld() { if( gIsEndShow ) M_End(); else GoToNextSld() } function M_GoPrevSld() { if( gIsEndShow ) { gIsEndShow=3D0; history.back();= PPTSld.event.cancelBubble=3Dtrue; } else GoToPrevSld() } function M_True() { return true } function M_End() { window.close( self ) } function CreateMenuItem( node,text,action,eval ) { var e=3DCreateItem( node ) e.type=3D"menuitem" e.Action=3Daction e.IsActive=3Deval e.innerHTML=3Dtext if( !e.IsActive() ) e.style.color=3D"threedshadow" e.onclick=3DPerform e.onmouseover=3DHighlight e.onmouseout=3DDeselect s=3De.style; 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charset="us-ascii" Review on Factoring ------=_NextPart_01C8FD9E.94234A60 Content-Location: file:///C:/A0C234E9/2factoringtrinomialI_files/outline.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii"
 No= tes
Slide Show
Outline
------=_NextPart_01C8FD9E.94234A60 Content-Location: file:///C:/A0C234E9/2factoringtrinomialI_files/filelist.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8FD9E.94234A60--