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 6.6 Factoring  by Grouping

(Examples provided by Prentice Hall)

Part I: Factoring by Grouping

 

Example 1		2x3 + 6x2 + x + 3 = 2x2(x + 3) + 1(x + 3)  = (2x2 + 1)(x + 3)
Example 2	4a3 + 10a2 + 6a + 15  = 2a2(x + 3) + 1(x + 3)  = (2a2 + 3)(2a + 5)
Example 3	5x4 – 5x3 – x + 1 = 5x3(x – 1) – 1(x – 1)  = (5x3 – 1)(x – 1)
Example 4	2x3 + 2x2 – 8x – 8 = 2(x3 + x2 – 4x – 4)  = 2[x(x2 – 4) + 1(x2 – 4)]  = 2(x + 1)(x2 – 4)  = 2(x + 1)(x + 2)(x – 2)
Example 5	4x3 + 3x2 + 2x + 1 = x3(4x + 3) + 2x + 1 This method doesn't work in this case.

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