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P.4 Factoring Polynomials Factor each expression (means factor COMPLETELY) a. 6x 3 – 4x b. − 4x 2 + 12x – 16 c. (x – 2)(2x) + (x – 2)(3) 2x(3x 2 ) – 2x(2)

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Presentation on theme: "P.4 Factoring Polynomials Factor each expression (means factor COMPLETELY) a. 6x 3 – 4x b. − 4x 2 + 12x – 16 c. (x – 2)(2x) + (x – 2)(3) 2x(3x 2 ) – 2x(2)"— Presentation transcript:

1 P.4 Factoring Polynomials Factor each expression (means factor COMPLETELY) a. 6x 3 – 4x b. − 4x x – 16 c. (x – 2)(2x) + (x – 2)(3) 2x(3x 2 ) – 2x(2) =2x(3x 2 – 2) -4(x 2 ) + (-4)(-3x) + (-4)(4) -4(x 2 − 3x + 4) (x – 2)(2x + 3)

2 Ex. 2 Factor completely 3 – 12x 2 Difference of two squares: Perfect squares trinomial: Sum or difference of two cubes: x 2 – y 2 = (x + y)(x – y) x 2 + 2xy + y 2 = (x + y) 2 x 2 − 2xy + y 2 = (x − y) 2 x 3 + y 3 = (x + y)(x 2 – xy + y 2 ) 3(1) – 3(4x 2 ) =3(1 – 4x 2 ) =3(1 – 2x)(1 + 2x) x 3 − y 3 = (x − y)(x 2 + xy + y 2 )

3 Ex. 3 Factor completely. a. (x + 4) 2 – y 2 b. 16x 4 – 81 Ex. 4 Factor completely. a. x 2 – 10x + 25 b. 16x x + 9 (x + 4) 2 – y 2 =[(x + 4) – y] [(x + 4) + y] (x + 4 – y)( x y) (4x 2 ) 2 – 9 2 =(4x 2 – 9) (4x 2 + 9) =[(2x) 2 – 3 2 ] (4x 2 + 9) =(2x – 3) (2x + 3) (4x 2 + 9) = x 2 – 2(5x) =(x – 5) 2 = (4x) 2 + 2(4x)(3) =(4x + 3) 2

4 Ex. 7 Factor completely. x 2 – 7x + 12 WHAT MULTIPLIES TO GET 12? AND ADDS TO GET 7? + (X 3)(X 4)–– Pg. 38 _____________________________________________


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