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Algebraic Expressions
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An algebraic expression is a formula constructed with variables and numbers = using additon, subtraction, multiplication, division, and taking roots.
Algebraic Expressions
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An algebraic expression is a formula constructed with variables and numbers = using additon, subtraction, multiplication, division, and taking roots.
Algebraic Expressions
Examples = of algebraic expressions are
3x= 2 – 2x + 4,
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An algebraic expression is a formula constructed with variables and numbers = using additon, subtraction, multiplication, division, and taking roots.
Algebraic Expressions
Examples = of algebraic expressions are
3x= 2 – 2x + 4,
x<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 + 3
Ö3 x – 2x – 4
,<= /div>
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An algebraic expression is a formula constructed with variables and numbers = using additon, subtraction, multiplication, division, and taking roots.
Algebraic Expressions
Examples = of algebraic expressions are
3x= 2 – 2x + 4,
x<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 + 3
Ö3 x – 2x – 4
,<= /div>
(x= 1/2 + y)1/3
(4y2 – (x + 4)1/2) 
------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0126_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhdQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABz AAEAgAAAAAAAAAIJjI+py+0Po3QFADs= ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0126_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0126_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACh AAEAgAAAAAAAAAILjI+py+0Po5y0sgIAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0127.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
An algebraic expression is a formula constructed with variables and numbers = using additon, subtraction, multiplication, division, and taking roots.
Algebraic Expressions
Examples = of algebraic expressions are
3x= 2 – 2x + 4,
x<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 + 3
Ö3 x – 2x – 4
,<= /div>
(x= 1/2 + y)1/3
(4y2 – (x + 4)1/2) 
Examples = of non-algebraic expressions are
sin(x), 2= x, log(x + 1).
------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0127_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhdQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABz AAEAgAAAAAAAAAIJjI+py+0Po3QFADs= ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0127_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0127_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhowACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACh AAEAgAAAAAAAAAILjI+py+0Po5y0sgIAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0128.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
An algebraic expression is a formula constructed with variables and numbers = using additon, subtraction, multiplication, division, and taking roots.
Algebraic Expressions
Examples = of algebraic expressions are
3x= 2 – 2x + 4,
x<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 + 3
Ö3 x – 2x – 4
,<= /div>
(x= 1/2 + y)1/3
(4y2 – (x + 4)1/2) 
Examples = of non-algebraic expressions are
sin(x), 2= x, log(x + 1).
The algeb= raic expressions anxn + an-1xn-1...+ a1x + a= 0 
where ai are numbers, are called polynomials (in x).<= /span>
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An algebraic expression is a formula constructed with variables and numbers = using additon, subtraction, multiplication, division, and taking roots.
Algebraic Expressions
Examples = of algebraic expressions are
3x= 2 – 2x + 4,
x<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 + 3
Ö3 x – 2x – 4
,<= /div>
(x= 1/2 + y)1/3
(4y2 – (x + 4)1/2) 
Examples = of non-algebraic expressions are
sin(x), 2= x, log(x + 1).
The algeb= raic expressions anxn + an-1xn-1...+ a1x + a= 0 
where ai are numbers, are called polynomials (in x).<= /span>
The algeb= raic expressions      where P and Q are
polynomia= ls, are called rational expression.
P
Q
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
Example A: Expand= and simplify.
(2x – 5)(x = +3) – (3x – 4)(x + 5)
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
Example A: Expand= and simplify.
(2x – 5)(x = +3) – [(3x – 4)(x + 5)]
Insert [     ]=
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
Example A: Expand= and simplify.
(2x – 5)(x = +3) – [(3x – 4)(x + 5)]
=3D   2x2 + x – 15 –= ; [3x2 + 11x – 20]
Insert [     ]=
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
Example A: Expand= and simplify.
(2x – 5)(x = +3) – [(3x – 4)(x + 5)]
=3D   2x2 + x – 15 –= ; [3x2 + 11x – 20]
=3D   2x2 + x – 15 – 3x2 – 11x + 20
Insert [     ]=
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
Example A: Expand= and simplify.
(2x – 5)(x = +3) – [(3x – 4)(x + 5)]
=3D   2x2 + x – 15 –= ; [3x2 + 11x – 20]
=3D   2x2 + x – 15 – 3x2 – 11x + 20
=3D   –x2 – 10x + 5
Insert [     ]=
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
Example A: Expand= and simplify.
(2x – 5)(x = +3) – [(3x – 4)(x + 5)]
=3D   2x2 + x – 15 –= ; [3x2 + 11x – 20]
=3D   2x2 + x – 15 – 3x2 – 11x + 20
=3D   –x2 – 10x + 5
Insert [     ]=
To factor an expre= ssion means to write it as a product in a nontrivial way. 
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Polynomial Expressions
Following= are examples of operations with
polynomia= ls and rational expressions.
Example A: Expand= and simplify.
(2x – 5)(x = +3) – [(3x – 4)(x + 5)]
=3D   2x2 + x – 15 –= ; [3x2 + 11x – 20]
=3D   2x2 + x – 15 – 3x2 – 11x + 20
=3D   –x2 – 10x + 5
Insert [     ]=
A    B3 = =3D (A    B)(A2    AB + B2)
Important Factoring Formulas:
To factor an expre= ssion means to write it as a product in a nontrivial way. 
A – B2 = =3D (A + B)(A – B)
+
–
+
–
+
–
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Example B. Factor 64x3 + 125
Polynomial Expressions
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Example B. Factor 64x3 + 125
64x3 + 125        
=3D (4x)3 + (5)3
Polynomial Expressions
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Example B. Factor 64x3 + 125
64x3 + 125        
=3D (4x)3 + (5)3
=3D (4x + 5)((4x)2 – (4x)(5) +(5)2)
Polynomial Expressions
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Example B. Factor 64x3 + 125
64x3 + 125        
=3D (4x)3 + (5)3
=3D (4x + 5)((4x)2 – (4x)(5) +(5)2)   
=3D (4x + 5)(16x2 – 20x + 25)
Polynomial Expressions
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Example B. Factor 64x3 + 125
64x3 + 125        
=3D (4x)3 + (5)3
=3D (4x + 5)((4x)2 – (4x)(5) +(5)2)   
=3D (4x + 5)(16x2 – 20x + 25)
Polynomial Expressions
We factor polynomials for many purposes:
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Example B. Factor 64x3 + 125
64x3 + 125        
=3D (4x)3 + (5)3
=3D (4x + 5)((4x)2 – (4x)(5) +(5)2)   
=3D (4x + 5)(16x2 – 20x + 25)
Polynomial Expressions
We factor polynomials for many purposes:
I. to or check for the sign of the output or to calculate
the output.
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Example B. Factor 64x3 + 125
64x3 + 125        
=3D (4x)3 + (5)3
=3D (4x + 5)((4x)2 – (4x)(5) +(5)2)   
=3D (4x + 5)(16x2 – 20x + 25)
Polynomial Expressions
We factor polynomials for many purposes:
I. to or check for the sign of the output or to calculate
the output.
II. to simplify or perform algebraic operations with
rational expressions. 
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Example B. Factor 64x3 + 125
64x3 + 125        
=3D (4x)3 + (5)3
=3D (4x + 5)((4x)2 – (4x)(5) +(5)2)   
=3D (4x + 5)(16x2 – 20x + 25)
Polynomial Expressions
We factor polynomials for many purposes:
I. to or check for the sign of the output or to calculate
the output.
II. to simplify or perform algebraic operations with
rational expressions. 
III. to solve equations (See next section).
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Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  <= /span>
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Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
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Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
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Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
2x3 – 5x2 + 2x =3D x(2x2 – 5x + 2)
=3D x(2x= – 1)(x – 2)
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
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Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
2x3 – 5x2 + 2x =3D x(2x2 – 5x + 2)
=3D x(2x= – 1)(x – 2)
For x =3D -2:
-2 [2(-2) – 1] [(-2) – 2]
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
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Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
2x3 – 5x2 + 2x =3D x(2x2 – 5x + 2)
=3D x(2x= – 1)(x – 2)
For x =3D -2:
-2 [2(-2) – 1] [(-2) – 2] =3D -2 [-5] [-4] =3D -40
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0213_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAq ABwAgAAAAAAAAAJHjI+pywsPo5y0RmOzznj7332iFY7mFZwqVK5j64JpbMK0Zt/krHt5P/kBUcON sAg4FpVDJtDZg+qkNyrNGsO6tKtU4wv+AgoAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0214.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
2x3 – 5x2 + 2x =3D x(2x2 – 5x + 2)
=3D x(2x= – 1)(x – 2)
For x =3D -2:
-2 [2(-2) – 1] [(-2) – 2] =3D -2 [-5] [-4] =3D -40
For x =3D -1:
-1 [2(-1) – 1] [(-1) – 2]
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0214_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAq ABwAgAAAAAAAAAJHjI+pywsPo5y0RmOzznj7332iFY7mFZwqVK5j64JpbMK0Zt/krHt5P/kBUcON sAg4FpVDJtDZg+qkNyrNGsO6tKtU4wv+AgoAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0215.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
2x3 – 5x2 + 2x =3D x(2x2 – 5x + 2)
=3D x(2x= – 1)(x – 2)
For x =3D -2:
-2 [2(-2) – 1] [(-2) – 2] =3D -2 [-5] [-4] =3D -40
For x =3D -1:
-1 [2(-1) – 1] [(-1) – 2] =3D -1 [-3] [-3] =3D -9
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0215_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAq ABwAgAAAAAAAAAJHjI+pywsPo5y0RmOzznj7332iFY7mFZwqVK5j64JpbMK0Zt/krHt5P/kBUcON sAg4FpVDJtDZg+qkNyrNGsO6tKtU4wv+AgoAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0215_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAq ABwAgAAAAAAAAAJKRI6py50Gopy02jsP3nzrDoZfSGJjiWZBykpnW76wuM6obHN4btY8uPtVgkJV sUM8GnxKS/L4LEaF01+Vd81lbdtZF7ZyiMdiQAEAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0216.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
2x3 – 5x2 + 2x =3D x(2x2 – 5x + 2)
=3D x(2x= – 1)(x – 2)
For x =3D -2:
-2 [2(-2) – 1] [(-2) – 2] =3D -2 [-5] [-4] =3D -40
For x =3D -1:
-1 [2(-1) – 1] [(-1) – 2] =3D -1 [-3] [-3] =3D -9
For x =3D 3:
3 [2(3) – 1] [(3) – 2]
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0216_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAq ABwAgAAAAAAAAAJHjI+pywsPo5y0RmOzznj7332iFY7mFZwqVK5j64JpbMK0Zt/krHt5P/kBUcON sAg4FpVDJtDZg+qkNyrNGsO6tKtU4wv+AgoAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0216_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAq ABwAgAAAAAAAAAJKRI6py50Gopy02jsP3nzrDoZfSGJjiWZBykpnW76wuM6obHN4btY8uPtVgkJV sUM8GnxKS/L4LEaF01+Vd81lbdtZF7ZyiMdiQAEAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0217.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Example C: Evaluate 2x – 5x2 = + 2x for x =3D -2, -1, 3  <= /span><= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:156%;color:#006600;mso-fareast-language:ZH-CN'>by factorin= g it first.
2x3 – 5x2 + 2x =3D x(2x2 – 5x + 2)
=3D x(2x= – 1)(x – 2)
For x =3D -2:
-2 [2(-2) – 1] [(-2) – 2] =3D -2 [-5] [-4] =3D -40
For x =3D -1:
-1 [2(-1) – 1] [(-1) – 2] =3D -1 [-3] [-3] =3D -9
For x =3D 3:
3 [2(3) – 1] [(3) – 2] =3D 3 [5] [1] =3D 15
Evaluate Polynom= ial Expressions
Its easier to evaluate factored polynomial expressions.  It takes= less number of steps then plugging in the values directly.  
------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0217_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAq ABwAgAAAAAAAAAJHjI+pywsPo5y0RmOzznj7332iFY7mFZwqVK5j64JpbMK0Zt/krHt5P/kBUcON sAg4FpVDJtDZg+qkNyrNGsO6tKtU4wv+AgoAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0217_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAq ABwAgAAAAAAAAAJKRI6py50Gopy02jsP3nzrDoZfSGJjiWZBykpnW76wuM6obHN4btY8uPtVgkJV sUM8GnxKS/L4LEaF01+Vd81lbdtZF7ZyiMdiQAEAOw== ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0217_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgAdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAp ABsAgAAAAAAAAAJDjI+pywoPo5y0QmOztnh7331iFY7mFZzqU65i64JpPMJ0Zt/krG95L/kBUUON sHgcJoHLXlP3vEVp01jVdV01ttxuAQA7 ------=_NextPart_01C82E61.4D2A43A0 Content-Location: file:///C:/2D664A33/2AlgebraicExpressions_files/slide0204.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
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Example D: Determ= ine the outcome is + or  –<= span style=3D'mso-spacerun:yes'> 
for x2 – 2x – 3 if x =3D -3/2= .
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
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Example D: Determ= ine the outcome is + or  –<= span style=3D'mso-spacerun:yes'> 
for x2 – 2x – 3 if x =3D -3/2= .
x2 – 2x – 3 =3D (x –= ; 3)(x + 1). 
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
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Example D: Determ= ine the outcome is + or  –<= span style=3D'mso-spacerun:yes'> 
for x2 – 2x – 3 if x =3D -3/2= .
x2 – 2x – 3 =3D (x –= ; 3)(x + 1).  Hence for x =3D -3/2,
we get (-3/2 – 3)(-3/2 + 1)
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
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Example D: Determ= ine the outcome is + or  –<= span style=3D'mso-spacerun:yes'> 
for x2 – 2x – 3 if x =3D -3/2= .
x2 – 2x – 3 =3D (x –= ; 3)(x + 1).  Hence for x =3D -3/2,
we get (-3/2 – 3)(-3/2 + 1) is (–)(–) =3D + .
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
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Example D: Determ= ine the outcome is + or  –<= span style=3D'mso-spacerun:yes'> 
for x2 – 2x – 3 if x =3D -3/2= .
x2 – 2x – 3 =3D (x –= ; 3)(x + 1).  Hence for x =3D -3/2,
we get (-3/2 – 3)(-3/2 + 1) is (–)(–) =3D + .
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
Rational Express= ions
We say a rational expression is in the factored form
if it's numerator and denominator are factored.
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Example D: Determ= ine the outcome is + or  –<= span style=3D'mso-spacerun:yes'> 
for x2 – 2x – 3 if x =3D -3/2= .
x2 – 2x – 3 =3D (x –= ; 3)(x + 1).  Hence for x =3D -3/2,
we get (-3/2 – 3)(-3/2 + 1) is (–)(–) =3D + .
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
Rational Express= ions
We say a rational expression is in the factored form
if it's numerator and denominator are factored.
Example E. Factor
x– 1
x – 3x+ 2
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Example D: Determ= ine the outcome is + or  –<= span style=3D'mso-spacerun:yes'> 
for x2 – 2x – 3 if x =3D -3/2= .
x2 – 2x – 3 =3D (x –= ; 3)(x + 1).  Hence for x =3D -3/2,
we get (-3/2 – 3)(-3/2 + 1) is (–)(–) =3D + .
Determine the Signs of the Outputs.
Its much easier to fin= d out whether the sign of a when evaluating a value using the factored for= m.
Rational Express= ions
We say a rational expression is in the factored form
if it's numerator and denominator are factored.
Example E. Factor
x– 1
x – 3x+ 2
x– 1
x – 3x+ 2
=3D
(x – 1)(x + 1)
(x – 1)(x – 2)
is the factored form.
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Rational Express= ions
We put the rational expressions in the factored form
in order to reduce, multiply or divide them.  
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Rational Express= ions
We put the rational expressions in the factored form
in order to reduce, multiply or divide them.  
Cancellation Rule:  Given an rational expression = ;
in the factored form, common factor may be cancelled,
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Rational Express= ions
We put the rational expressions in the factored form
in order to reduce, multiply or divide them.  
Cancellation Rule:  Given an rational expression = ;
in the factored form, common factor may be cancelled,
in symbol  
x*y
x*z
=3D
x*y
x*z
=3D
y
z
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Rational Express= ions
We put the rational expressions in the factored form
in order to reduce, multiply or divide them.  
Cancellation Rule:  Given an rational expression = ;
in the factored form, common factor may be cancelled,
in symbol  
x*y
x*z
=3D
x*y
x*z
=3D
y
z
An rational expression that can't be cancelled any further is said to be reduced.
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Rational Express= ions
We put the rational expressions in the factored form
in order to reduce, multiply or divide them.  
Example F. Reduce
x– 1
x – 3x+ 2
Cancellation Rule:  Given an rational expression = ;
in the factored form, common factor may be cancelled,
in symbol  
x*y
x*z
=3D
x*y
x*z
=3D
y
z
An rational expression that can't be cancelled any further is said to be reduced.
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Rational Express= ions
We put the rational expressions in the factored form
in order to reduce, multiply or divide them.  
Example F. Reduce
x– 1
x – 3x+ 2
x– 1
x – 3x+ 2
=3D