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Factoring Polynomials Factoring Polynomials Factoring Polynomials

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Example 1 Find factorizations of 6x 2. (1)(6x 2 )(2)(3x 2 ) (6)(x 2 )(1x)(6x) (2x)(3x) (-1)(-6x 2 )(-2)(-3x 2 )(-3)(-2x 2 )

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Example 2 Factor. a) 5x ( )x3x3 + 2 b) 6x x 2 6x 2 ( )x + 2 c) 12u 3 v uv 4 4uv 2 ( ) 3u 2 + 4v 2

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Practice Factor. 1) x 2 + 3x 2) a 2 b + 2ab

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Example 3 Factor. d) 18y 4 – 6y y 2 e) 8x 4 y 3 – 6x 2 y 4 f) 5x 3 y 4 + 7x 2 z 3 + 3y 2 z

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Example 3 Factor. d) 18y 4 – 6y y 2 6y 2 ( ) 3y 2 - y e) 8x 4 y 3 – 6x 2 y 4 2x 2 y 3 ( )4x 2 - 3y f) 5x 3 y 4 + 7x 2 z 3 + 3y 2 z + 2 No common factors

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Practice Factor. 1) 3x 6 – 5x 3 + 2x 2 2) 9x 4 – 15x 3 + 3x 2

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Practice Factor. 3) 2p 3 q 2 + p 2 q + pq 4) 12m 4 n 4 + 3m 3 n 2 + 6m 2 n 2

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Factor by Grouping When polynomials contain four terms, it is sometimes easier to group like terms in order to factor. Your goal is to create a common factor. You can also move terms around in the polynomial to create a common factor. Practice makes you better in recognizing common factors.

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Factoring Four Term Polynomials

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Factor by Grouping FACTOR: 3xy - 21y + 5x – 35 Factor the first two terms: 3xy - 21y = 3y (x – 7) Factor the last two terms: + 5x - 35 = 5 (x – 7) The green parentheses are the same so its the common factor Now you have a common factor (x - 7) (3y + 5)

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Factor by Grouping FACTOR: 6mx – 4m + 3rx – 2r Factor the first two terms: 6mx – 4m = 2m (3x - 2) Factor the last two terms: + 3rx – 2r = r (3x - 2) The green parentheses are the same so its the common factor Now you have a common factor (3x - 2) (2m + r)

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Factor by Grouping FACTOR: 15x – 3xy + 4y –20 Factor the first two terms: 15x – 3xy = 3x (5 – y) Factor the last two terms: + 4y –20 = 4 (y – 5) The green parentheses are opposites so change the sign on the (-y + 5) or – 4 (5 - y) Now you have a common factor (5 – y) (3x – 4)

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