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**P.4 Factoring Polynomials**

Factor each expression (means factor COMPLETELY) a. 6x3 – 4x b. −4x2 + 12x – 16 c. (x – 2)(2x) + (x – 2)(3) 2x(3x2) – 2x(2) = 2x(3x2 – 2) -4(x2) + (-4)(-3x) + (-4)(4) -4(x2 − 3x + 4) (x – 2)(2x + 3)

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**Difference of two squares: Perfect squares trinomial:**

Sum or difference of two cubes: x2 – y2 = (x + y)(x – y) x2 + 2xy + y2 = (x + y)2 x2 − 2xy + y2 = (x − y)2 x3 + y3 = (x + y)(x2 – xy + y2) x3 − y3 = (x − y)(x2 + xy + y2) Ex Factor completely 3 – 12x2 3(1) – 3(4x2) = 3(1 – 4x2) = 3(1 – 2x)(1 + 2x)

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**Ex. 3 Factor completely. a. (x + 4)2 – y2 b. 16x4 – 81**

a. x2 – 10x + 25 b x2 + 24x + 9 (x + 4)2 – y2 = [(x + 4) – y] [(x + 4) + y] (x + 4 – y)( x y) (4x2)2 – 92 = (4x2 – 9) (4x2 + 9) =[(2x)2 – 32] (4x2 + 9) =(2x – 3) (2x + 3) (4x2 + 9) = x2 – 2(5x) + 52 = (x – 5)2 = (4x)2 + 2(4x)(3) + 32 = (4x + 3)2

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**Ex. 7 Factor completely. x2 – 7x + 12 +**

AND ADDS TO GET 7? WHAT MULTIPLIES TO GET 12? (X 3)(X 4) – – Pg. 38 _____________________________________________

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Notes Over 10.8 BinomialTrinomial4 or more terms Methods of Factoring GCF Difference of Squares Perfect Square Trinomial Two Binomials (Shortcut) Two.

Notes Over 10.8 BinomialTrinomial4 or more terms Methods of Factoring GCF Difference of Squares Perfect Square Trinomial Two Binomials (Shortcut) Two.

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