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Example A.
2 + 3x à  “the sum of 2 and 3 times x”
4x2 – 5x à  “the difference between 4 times the square of x and 5 times x”
(3 – 2x)2  à “the square of the difference between 3 and twice = of x”
A mathematics expression is a calculation procedure written in numbers, variables, and operati= on symbols.
Expressions II
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Example A.
2 + 3x à  “the sum of 2 and 3 times x”
4x2 – 5x à  “the difference between 4 times the square of x and 5 times x”
(3 – 2x)2  à “the square of the difference between 3 and twice = of x”
A mathematics expression is a calculation procedure written in numbers, variables, and operati= on symbols.
Expressions II
An expression of the form #xN, w= here the exponent N is a
non-negative integer and  # is a number, is called a monomial = (one-term).
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Example A.
2 + 3x à  “the sum of 2 and 3 times x”
4x2 – 5x à  “the difference between 4 times the square of x and 5 times x”
(3 – 2x)2  à “the square of the difference between 3 and twice = of x”
A mathematics expression is a calculation procedure written in numbers, variables, and operati= on symbols.
Expressions II
An expression of the form #xN, w= here the exponent N is a non-negative integer and  # is a number, is called a monomial (one-term).
For example, 3x2, –4x3, and 5x6 are monomials.
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Example A.
2 + 3x à  “the sum of 2 and 3 times x”
4x2 – 5x à  “the difference between 4 times the square of x and 5 times x”
(3 – 2x)2  à “the square of the difference between 3 and twice = of x”
A mathematics expression is a calculation procedure written in numbers, variables, and operati= on symbols.
Expressions II
Example B.   Evaluate the monomia= ls if y =3D –4
a. 3y2  <= /span>
An expression of the form #xN, w= here the exponent N is a non-negative integer and  # is a number, is called a monomial (one-term).
For example, 3x2, –4x3, and 5x6 are monomials.
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Example A.
2 + 3x à  “the sum of 2 and 3 times x”
4x2 – 5x à  “the difference between 4 times the square of x and 5 times x”
(3 – 2x)2  à “the square of the difference between 3 and twice = of x”
A mathematics expression is a calculation procedure written in numbers, variables, and operati= on symbols.
Expressions II
Example B.   Evaluate the monomia= ls if y =3D –4
a. 3y2        = ;            &n= bsp;                = 3;
       3y2 = à 3(–4)2 
An expression of the form #xN, w= here the exponent N is a non-negative integer and  # is a number, is called a monomial (one-term).
For example, 3x2, –4x3, and 5x6 are monomials.
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Example A.
2 + 3x à  “the sum of 2 and 3 times x”
4x2 – 5x à  “the difference between 4 times the square of x and 5 times x”
(3 – 2x)2  à “the square of the difference between 3 and twice = of x”
A mathematics expression is a calculation procedure written in numbers, variables, and operati= on symbols.
Expressions II
Example B.   Evaluate the monomia= ls if y =3D –4
a. 3y2        = ;            &n= bsp;                = 3;
       3y2 = à 3(–4)2        = ;                     = 3;
       =3D 3(16) =3D 48        = ;       
An expression of the form #xN, w= here the exponent N is a non-negative integer and  # is a number, is called a monomial (one-term).
For example, 3x2, –4x3, and 5x6 are monomials.
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Expressions II
b. –3= y2      (y =3D –4)
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3= y3
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3 = 3;
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64)
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64) =3D 192
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64) =3D 192
Polynomial Expressions
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64) =3D 192
The sum of monomials are called= polynomials (many-terms), these are expressions of the form     
        = ;    #xN ± #xN-1 ± … ± #x1<= span style=3D'mso-bidi-font-family:Arial'> ± #
where # can be any number.
Polynomial Expressions
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64) =3D 192
The sum of monomials are called= polynomials (many-terms), these are expressions of the form     
        = ;    #xN ± #xN-1 ± … ± #x1<= span style=3D'mso-bidi-font-family:Arial'> ± #
where # can be any number.
For example, 4x + 7, 
Polynomial Expressions
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64) =3D 192
The sum of monomials are called= polynomials (many-terms), these are expressions of the form     
        = ;    #xN ± #xN-1 ± … ± #x1<= span style=3D'mso-bidi-font-family:Arial'> ± #
where # can be any number.
For example, 4x + 7,  –3x2 – 4x + 7= ,
Polynomial Expressions
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64) =3D 192
The sum of monomials are called= polynomials (many-terms), these are expressions of the form     
        = ;    #xN ± #xN-1 ± … ± #x1<= span style=3D'mso-bidi-font-family:Arial'> ± #
where # can be any number.
For example, 4x + 7,  –3x2 – 4x + 7= , –5x4 + 1= are polynomials,
Polynomial Expressions
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Expressions II
b. –3y2      (y =3D –4)= 3;
      –3y2 à –3(–4)2   
      =3D –= 3(16) =3D –48. 
c. –3y3
      –3y3 à – 3(–4)3   
      =3D –= 3(–64) =3D 192
The sum of monomials are called= polynomials (many-terms), these are expressions of the form     
        = ;    #xN ± #xN-1 ± … ± #x1<= span style=3D'mso-bidi-font-family:Arial'> ± #
where # can be any number.
For example, 4x + 7,  –3x2 – 4x + 7= , –5x4 + 1= are polynomials,
x
1
is not a polynomial.
where as the expression<= span lang=3DEN-US style=3D'font-size:133%;mso-fareast-language:ZH-TW;mso-specia= l-format: lastCR;display:none'>
Polynomial Expressions
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3.
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
Set x =3D = (–3) in the expression,
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
Set x =3D = (–3) in the expression, we get   = 3;
4(–3)2 – 3(–3)3
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
Set x =3D = (–3) in the expression, we get   = 3;
4(–3)2 – 3(–3)3
=3D 4(9) – 3(–27)
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
Set x =3D = (–3) in the expression, we get   = 3;
4(–3)2 – 3(–3)3
=3D 4(9) – 3(–27)
=3D 36 + 81 =
=3D 117  = 3;
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
Set x =3D = (–3) in the expression, we get   = 3;
4(–3)2 – 3(–3)3
=3D 4(9) – 3(–27)
=3D 36 + 81 =
=3D 117  = 3;
Given a polynomials, each monom= ial is called a term.
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
Set x =3D = (–3) in the expression, we get   = 3;
4(–3)2 – 3(–3)3
=3D 4(9) – 3(–27)
=3D 36 + 81 =
=3D 117  = 3;
Given a polynomials, each monom= ial is called a term.
<= /div>
        = ;     #xN ± #xN-1 ± … ± #x ± #
terms
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Expressions II
Example C.= Evaluate  the polynomial 4x2 – 3x3 = if x =3D –3.
The polynom= ial 4x2 – 3x3 is the combinatio= n of two monomials; 4x2  = and –3x3. When evaluating the polynomial, we evaluate each monomial then combine the results.
Set x =3D = (–3) in the expression, we get   = 3;
4(–3)2 – 3(–3)3
=3D 4(9) – 3(–27)
=3D 36 + 81 =
=3D 117  = 3;
Given a polynomials, each monom= ial is called a term.
<= /div>
        = ;     #xN ± #xN-1 ± … ± #x ± #
terms
Therefore= the polynomial –3x2 – 4x + 7 has 3 terms,
–3x= 2 , = –4x= and + 7.<= span lang=3DZH-CN style=3D'font-size:133%;mso-ansi-language:EN-US;mso-special-f= ormat: lastCR;display:none'>
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Expressions II
Each term is addressed by= the variable part. 
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2,
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, <= /span>
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, &= #13;
and the number term or the constant term<= /span> is 7.
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, &= #13;
and the number term or the constant term<= /span> is 7. 
The number infront of a term is called the coefficient of that term.
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, &= #13;
and the number term or the constant term<= /span> is 7. 
The number infront of a term is called the coefficient of that term. So the coefficient of –3x2 is –3 .
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, &= #13;
and the number term or the constant term<= /span> is 7. 
The number infront of a term is called the coefficient of that term. So the coefficient of –3x2 is –3 .
Operations with Polynomials
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, &= #13;
and the number term or the constant term<= /span> is 7. 
The number infront of a term is called the coefficient of that term. So the coefficient of –3x2 is –3 .
Terms with the same variabe part are called like-terms.
Operations with Polynomials
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, &= #13;
and the number term or the constant term<= /span> is 7. 
The number infront of a term is called the coefficient of that term. So the coefficient of –3x2 is –3 .
Terms with the same variabe part are called like-terms.
Like-terms may be combined.
Operations with Polynomials
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Expressions II
Each term is addressed by the variable part.  Hence the = 3;
x2-te= rm of the –3x2 – 4x + 7 is –3x2, the x-term is –4x, &= #13;
and the number term or the constant term<= /span> is 7. 
The number infront of a term is called the coefficient of that term. So the coefficient of –3x2 is –3 .
Terms with the same variabe part are called like-terms.
Like-terms may be combined.
For example, 4x + 5x =3D 9x
Operations with Polynomials
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