SPECIAL PRODUCTS AND FACTORING, P'3P'4 p' 2437

1
SPECIAL PRODUCTS AND FACTORING,(P.3-P.4) p. 24-37

• OBJECTIVES
• Write polynomials in standard form
• Add, subtract, and multiply polynomials
• Factor polynomials

2
Polynomials, p. 24

• Let a0,a1,a2,,an be real numbers.
• Let n be a nonnegative integer.
• Polynomial in x - an expression of the form
  (standard form)
• anxn an-1 x n-1 a1 x a0, where an is
  nonzero.
• Each akxk is a term with degree k and ak is the
  coefficient.
• The polynomial is of degree n ,
• an is the leading coefficient,
• a0 is the constant term.
• trinomials-three terms
• binomials-two terms
• monomials-one term

3
Operations with Polynomials, p. 25

• Addition- add like terms
• Subtraction- subtract like terms
• like terms- terms having the same variables to
  the same powers

Multiplication- (3x 1)(x 2) F
O I L
4
Special Products, p. 26

• Let u, v be real numbers, variables, or algebraic
  expressions.
• (u v)(u v) u2 v2
• (u v)2 u2 2uv v2
• (u v)2 u2 2uv v2

5
Factoring- the process of writing a polynomial as
a product, p. 33

• Polynomials with Common Factors
• 9x 6 3(3x 2)
• 4x2 16x 4x(x 4)

Factoring Special Polynomial Forms u2
v2 (u v)(u v) u2 2uv v2 (u v)2
u2 2uv v2 (u v)2
6
Express as a product of linear factors, called
factoring 9x2 12x 4 ( 3x ) (3x
) ( 3x 2 ) (3x 2)
-2
-2
Express as a product of linear factors, called
factoring x2 5x 6 ( x ) ( x
) ( x 3 ) ( x 2)
-3
-2
7
Express as a product of linear factors, called
factoring 2x2 7x 15 ( 2x ) ( x
) ( 2x 3 ) ( x 5 )
-3
5
8
Express as a product of linear factors, called
factoring 2x2 19x 33 ( 2x ) ( x
) (2x 3 ) ( x 11 )
3
-11
9
HOMEWORK

• p. 29-31 1-68, 73-99, 103-119 alt. odd
• p. 38-40 1-38, 47-101, 104-139 alt. odd
• Read p. 110-119 (1.4)
• PRE QUIZ (1.4)
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• Tutoring Walker 206 M-Th 430-630