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 6.1 Factoring Polynomials

Vocabulary

• prime number

• composite number

• common factor

• greatest common factor (GCF)

• prime factorization

(Examples provided by Prentice Hall)

Part I: Factoring Monomials

Find factorizations of the polynomials.

 

Example 1	6x2 (1)(6x2), (2)(3x2), (3)(2x2), (6)(x2),  (1x)(6x), (2x)(3x), (–1)(–6x2), (–2)(–3x2),  (–3)(–2x2), (–6)(–x2), (–1x)(–6x), (–2x)(–3x)
Example 2	6c2d (1)( 6c2d),   (c)(6cd),   (c2)(6d),  (2)(3c2d),   (2c)(3cd),   (2c2)(3d),   (3)(2c2d)

Part II: Factoring When Terms Have a Common Factor

 

Example 1	5x3 + 10  = 5(x3) + 5(2)  = 5(x3 + 2)
Example 2	6x3 + 12x2  = 6x2(x) + 6x2(2)  = 6x2(x + 2)
Example 3	12u3v2 + 16uv4  = 4uv2(3u2) + 4uv2(4v2)  = 4uv2(3u2 + 4v2)
Example 4	18y4 – 6y3 + 12y2  = 6y2(3y2) – 6y2(y) + 6y2(2)  = 6y2(3y2 – y + 2)
Example 5	8x4y3 – 6x2y4  = 2x2y3(4x2) – 2x2y3(3y)  = 2x2y3(4x2 – 3y)
Example 6	5x3y4 + 7x2z3 + 3y2z There is no common factor in this case.

Take class notes.