# P.4 Factoring Polynomials

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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)

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)

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

Ex. 7 Factor completely. x2 – 7x + 12 +
AND ADDS TO GET 7? WHAT MULTIPLIES TO GET 12? (X 3)(X 4) Pg. 38 _____________________________________________