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 6.9  Using Equations that Factor

(Examples provided by Prentice Hall)

The Principle of Zero Products

Solve.

 

Example 1		(x – 2)(x – 3) = 0 (x – 2) = 0   or   (x – 3) = 0 x = 2   or   x = 3
Example 2	3(x – 5)x = 0 (x – 5) = 0   or   x = 0 x = 5   or   x = 0
Example 3	(x – 2)(x – 3)(x – 4) = 0 (x – 2) = 0   or   (x – 3) = 0   or   (x – 4) = 0 x = 2   or   x = 3   or   x = 4

Part II: Factoring and Solving

Solve.

 

Example 1		x2 + 7x + 12 = 0 (x + 3)(x + 4) = 0 (x + 3) = 0   or   (x + 4) = 0 x = –3   or   x = –4
Example 2	x2 = –3x – 2 Rewrite as x2 + 3x + 2 = 0 and  factor as (x + 1)(x + 2) = 0 (x + 1) = 0   or   (x + 2) = 0 x = –1   or   x = –2
Example 3	x2 + 10x + 25 = 0 factors as (x + 5)2 = 0 (x + 5) = 0   or   (x + 5) = 0 x = –5   or   x = –5 There is only one solution in this case, –5.
Example 4	9x2 – 4 = 0 factors as (3x + 2)(3x – 2) = 0 (3x + 2) = 0   or   (3x – 2) = 0 3x = –2   or   3x = 2 x = – 2/3   or   x = 2/3

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