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To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
Pulling out G= CF
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
A = common factor of two or more quantities is a factor that
belongs t= o all the quantities.
Pulling out G= CF
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
Example A.
 = a. Since 6 =3D (2)(3) and 15 =3D (3)(5),
A = common factor of two or more quantities is a factor that
belongs t= o all the quantities.
Pulling out G= CF
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
Example A.
 = a. Since 6 =3D (2)(3) and 15 =3D (3)(5), so 3 = is a common factor.
A = common factor of two or more quantities is a factor that
belongs t= o all the quantities.
Pulling out G= CF
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
Example A.
 = a. Since 6 =3D (2)(3) and 15 =3D (3)(5), so 3 = is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.<= /span>
A = common factor of two or more quantities is a factor that
belongs t= o all the quantities.
Pulling out G= CF
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
Example A.
 = a. Since 6 =3D (2)(3) and 15 =3D (3)(5), so 3 = is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are 3, x, y2, xy2, ..
A = common factor of two or more quantities is a factor that
belongs t= o all the quantities.
Pulling out G= CF
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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±
±
–
+
To factor means to rewrite an expression as a product in= a nontrivial way. Following are the steps to factor an expression.
Review on Factor= ing
Example A.
 = a. Since 6 =3D (2)(3) and 15 =3D (3)(5), so 3 = is a common factor.
b. The common factor of 4ab, 6a are 2, a, 2a.&= #13;
c. The common factors of 6xy, 15x2y = are 3, x, y2, xy2, ..
d. The common factor of a(x+y), b(x+y) is (x+y= ).
A = common factor of two or more quantities is a factor that
belongs t= o all the quantities.
Pulling out G= CF
I. Always= pull out the greatest common factor first.
II. If the expression is a trinomial (three-term) ax2 + bx + c,
    use the reverse-FOIL method or the ac-method.
III. Use = the following factoring formulas if possible
x2 – y2 = =3D (x + y)(x – = y).
        = ;   x3     y3 =3D ( x    y )( x2    xy + y2 ).
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;  
Review on Factor= ing
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;   Pull the factor (x – y) again. =
   =3D (3 + a)(x – y= )
Review on Factor= ing
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
Reverse-FOIL (Guessing Method)
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;   Pull the factor (x – y) again. =
   =3D (3 + a)(x – y= )
Review on Factor= ing
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
Revers= e-FOIL (Guessing Method)
To factor= a trinomial (three-term) of the form ax + bx + c,
try an an= swer of the form (#x ± #) (#x ± #).
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;   Pull the factor (x – y) again. =
   =3D (3 + a)(x – y= )
Review on Factor= ing
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
Revers= e-FOIL (Guessing Method)
To factor= a trinomial (three-term) of the form ax + bx + c,
try an an= swer of the form (#x ± #) (#x ± #). To fin= d the correct a= nswer, we need to have(#)(#) =3D a,
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;   Pull the factor (x – y) again. =
   =3D (3 + a)(x – y= )
Review on Factor= ing
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
Revers= e-FOIL (Guessing Method)
To factor= a trinomial (three-term) of the form ax + bx + c,
try an an= swer of the form (#x ± #) (#x ± #). To fin= d the correct a= nswer, we need to have(#)(#) =3D a, (#)(#) =3D c
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;   Pull the factor (x – y) again. =
   =3D (3 + a)(x – y= )
Review on Factor= ing
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
Revers= e-FOIL (Guessing Method)
To factor= a trinomial (three-term) of the form ax + bx + c,
try an an= swer of the form (#x ± #) (#x ± #). To fin= d the correct a= nswer, we need to have(#)(#) =3D a, (#)(#) =3D c and <= /span>
that the = inner and outer products combined to be bx.
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;   Pull the factor (x – y) again. =
   =3D (3 + a)(x – y= )
Review on Factor= ing
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b. (2x ̵= 1; 3)3x – 2(2x – 3)
    Pull out the common f= actor (2x – 3),
    (2x – 3)<= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:75%;color:#003300;mso-fareast-language:ZH-CN'>3x – 2= (2x – 3) =3D = (2x – 3)(3x – = 2)
(the GCF is 6x2y)
Example C. Factor out the GCF.
a. 12x2y3 + 6x2y2 =3D 6x2y2(2y) + <= /span>6x2y2(1) =3D = 6x2y= 2(2y + 1)=
Revers= e-FOIL (Guessing Method)
To factor= a trinomial (three-term) of the form ax + bx + c,
try an an= swer of the form (#x ± #) (#x ± #). To fin= d the correct a= nswer, we need to have(#)(#) =3D a, (#)(#) =3D c and <= /span>
that the = inner and outer products combined to be bx.
That is (= #x ±= ; #) (#x ±= ; #).=
combined to be bx
=
c. 3x – 3y + ax – ay        = ;      Group them into two groups.
   =3D (3x – 3y) + (ax – ay)       Fac= tor out the GCF of each group.
   =3D 3(x – y) + a(x – y)        = ;   Pull the factor (x – y) again. =
   =3D (3 + a)(x – y= )
Review on Factor= ing
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2.
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4)
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, <= /span>
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
If the number term c i= n the trinomial is a prime number, start by setting the number = terms as 1 and c,
i.e. ax2 + bx + c =3D (#x  ± c)(#x ± 1)  
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
Example E.  Factor 20x2 – 4x – 3
If the number term c i= n the trinomial is a prime number, start by setting the number = terms as 1 and c,
i.e. ax2 + bx + c =3D (#x  ± c)(#x ± 1)  
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
Example E.  Factor 20x2 – 4x – 3 <= /div>
Since 3 =3D (3)(1), it must be (   ± 3 ) (   ± 1 ) to get the –3.
If the number term c i= n the trinomial is a prime number, start by setting the number = terms as 1 and c,
i.e. ax2 + bx + c =3D (#x  ± c)(#x ± 1)  
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
Example E.  Factor 20x2 – 4x – 3 <= /div>
Since 3 =3D (3)(1), it must be (   ± 3 ) (   ± 1 ) to get the –3.
20 =3D (1)(20) =3D (2)(10) =3D (4)(5),
If the number term c i= n the trinomial is a prime number, start by setting the number = terms as 1 and c,
i.e. ax2 + bx + c =3D (#x  ± c)(#x ± 1)  
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
Example E.  Factor 20x2 – 4x – 3 <= /div>
Since 3 =3D (3)(1), it must be (   ± 3 ) (   ± 1 ) to get the –3.
20 =3D (1)(20) =3D (2)(10) =3D (4)(5), observe that t= he difference
between (2)(3) and (10)(1) is ±4
If the number term c i= n the trinomial is a prime number, start by setting the number = terms as 1 and c,
i.e. ax2 + bx + c =3D (#x  ± c)(#x ± 1)  
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
Example E.  Factor 20x2 – 4x – 3 <= /div>
Since 3 =3D (3)(1), it must be (   ± 3 ) (   ± 1 ) to get the –3.
20 =3D (1)(20) =3D (2)(10) =3D (4)(5), observe that t= he difference
between (2)(3) and (10)(1) is ±4 which matches the coeffici= ent of the middle term –4x.  <= /span>
If the number term c i= n the trinomial is a prime number, start by setting the number = terms as 1 and c,
i.e. ax2 + bx + c =3D (#x  ± c)(#x ± 1)  
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Review on Factor= ing
Example D.  Factor x2 – 4x – 12 =
We are to fill in (       x ±       ) (      <= /span> x ±       ). 
It must be (1x ±       ) (1x ±       ) to get the 1x2. Furthermore,
it must be (x +       ) (x –       ) to get the –12.
12 =3D (1)(12) =3D (2)(6) =3D (3)(4) and the difference between 2 and = 6 is ±4 which matches the coefficient of the middle term –4x, 
we see that x – 4x – 12 =3D (x + 2)(x – 6)
Example E.  Factor 20x2 – 4x – 3 <= /div>
Since 3 =3D (3)(1), it must be (   ± 3 ) (   ± 1 ) to get the –3.
20 =3D (1)(20) =3D (2)(10) =3D (4)(5), observe that t= he difference
between (2)(3) and (10)(1) is ±4 which matches the coeffici= ent of the middle term –4x. Use 2 and 10 for the
x-terms, we get 20x – 4x – 3 =3D (<= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >10x + 3)(2x – 1 )
If the number term c i= n the trinomial is a prime number, start by setting the number = terms as 1 and c,
i.e. ax2 + bx + c =3D (#x  ± c)(#x ± 1)  
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The ac-Method
The produ= ct of two binomials has four terms.  We may use grouping-method to work backward to o= btain the two binomials. 
Example F.  Factor x2 – x – 6 by grouping.&#= 13;
x2 – x – 6
=3D x2 – 3x + 2x – 6        = ;   Put them into two groups
=3D (x2 – 3x) + (2x – 6)      Take out = the common factor
=3D x(x – 3) + 2(x – 3)      
Review on Factor= ing
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The ac-Method
The produ= ct of two binomials has four terms.  We may use grouping-method to work backward to o= btain the two binomials. 
Example F.  Factor x2 – x – 6 by grouping.&#= 13;
x2 – x – 6
=3D x2 – 3x + 2x – 6        = ;   Put them into two groups
=3D (x2 – 3x) + (2x – 6)      Take out = the common factor
=3D x(x – 3) + 2(x – 3)       Tak= e out the common (x – 3)
=3D (x – 3)(x + 2)
Review on Factor= ing
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The ac-Method
The produ= ct of two binomials has four terms.  We may use grouping-method to work backward to o= btain the two binomials. 
But how do we know to = write x2 – x – 6 as x2 – 3x + 2x – 6 in the first place? 
Example F.  Factor x2 – x – 6 by grouping.&#= 13;
x2 – x – 6
=3D x2 – 3x + 2x – 6        = ;   Put them into two groups
=3D (x2 – 3x) + (2x – 6)      Take out = the common factor
=3D x(x – 3) + 2(x – 3)       Tak= e out the common (x – 3)
=3D (x – 3)(x + 2)
Review on Factor= ing
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The ac-Method
The produ= ct of two binomials has four terms.  We may use grouping-method to work backward to o= btain the two binomials. 
But how do we know to = write x2 – x – 6 as x2 – 3x + 2x – 6 in the first place?  This leads to the ac-method.
Example F.  Factor x2 – x – 6 by grouping.&#= 13;
x2 – x – 6
=3D x2 – 3x + 2x – 6        = ;   Put them into two groups
=3D (x2 – 3x) + (2x – 6)      Take out = the common factor
=3D x(x – 3) + 2(x – 3)       Tak= e out the common (x – 3)
=3D (x – 3)(x + 2)
Review on Factor= ing
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The ac-Method
The produ= ct of two binomials has four terms.  We may use grouping-method to work backward to o= btain the two binomials. 
But how do we know to = write x2 – x – 6 as x2 – 3x + 2x – 6 in the first place?  This leads to the ac-method. The ac-method tells us how to rewrit= e the trinomial so we may use the grouping method.
Example F.  Factor x2 – x – 6 by grouping.&#= 13;
x2 – x – 6
=3D x2 – 3x + 2x – 6        = ;   Put them into two groups
=3D (x2 – 3x) + (2x – 6)      Take out = the common factor
=3D x(x – 3) + 2(x – 3)       Tak= e out the common (x – 3)
=3D (x – 3)(x + 2)
Review on Factor= ing
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The ac-Method
The produ= ct of two binomials has four terms.  We may use grouping-method to work backward to o= btain the two binomials. 
But how do we know to = write x2 – x – 6 as x2 – 3x + 2x – 6 in the first place?  This leads to the ac-method. The ac-method tells us how to rewrit= e the trinomial so we may use the grouping method. If it= isn't possible to rewrite the trinomial according to the ac-me= thod, then the trinomial is prime.
Example F.  Factor x2 – x – 6 by grouping.&#= 13;
x2 – x – 6
=3D x2 – 3x + 2x – 6        = ;   Put them into two groups
=3D (x2 – 3x) + (2x – 6)      Take out = the common factor
=3D x(x – 3) + 2(x – 3)       Tak= e out the common (x – 3)
=3D (x – 3)(x + 2)
Review on Factor= ing
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ac-Method:<= span style=3D'mso-spacerun:yes'>  We assume that there is no common factor for the trinomial ax + bx + c.<= /span>
Review on Factor= ing
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ac-Method:<= span style=3D'mso-spacerun:yes'>  We assume that there is no common factor for the trinomial ax + bx + c.
1.  Calculate ac, =
Review on Factor= ing
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ac-Method:<= span style=3D'mso-spacerun:yes'>  We assume that there is no common factor for the trinomial ax + bx + c.
1.  Calculate ac, and fin= d two numbers u&v such that
     uv is ac, =
Review on Factor= ing
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ac-Method:<= span style=3D'mso-spacerun:yes'>  We assume that there is no common factor for the trinomial ax + b