Chapter Six:   Polynomials and Factoring

Take notes on the following topics.

Chapter Six

Section 6.1

Section 6.2

Section 6.3

Section 6.4

Section 6.5

Section 6.6

Section 6.7

Section 6.8

Section 6.9

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Section 6.2 Difference of Two Square

For a binomial to be the difference of two squares, two condition must hold.

(1) There must be two terms, both squares.

(2) There must be a minus sign between the two terms

(Examples provided by Prentice Hall)

Part I: Recognizing Differences of Two Squares

Rewrite as a difference of two squares.

 

Example 1	4x2 – 16y2  = (2x)2 – (4y)2
Example 2	9a2 + 6ab + b2 – 1  = (3a + b)2 – (1)2

Part II: Factoring Differences of Two Squares

Factor.

 

Example 1	y2 – 16  = (y + 4)(y – 4)
Example 2	25x2 – 4  = (5x)2 – 22 = (5x + 2)(5x – 2)
Example 3	25x4 – 64y2  = (5x2)2 – (8y)2  = (5x2 + 8y)(5x2 – 8y)
Example 4	32x2 – 50y2  = 2(16x2 – 25y2)  = 2[(4x)2 – (5y)2]  = 2(4x + 5y)(4x – 5y)

Part III: Factoring Completely

Factor.

 

Example 1

a4 – b4  = (a2)2 – (b2)2  = (a2 + b2)(a2 – b2)  = (a2 + b2)(a + b)(a – b) Note that a2 + b2 cannot be factored.

Take class notes.