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Solving polynomial Equations in Factored Form MM1A2f: Goal: solve polynomial equations Factor trinomials of the form x2 +bx +c

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Zero Product Property The zero-product property is used to solve an equation when one side is zero and the other side is a product of polynomial factors The zero-product property is used to solve an equation when one side is zero and the other side is a product of polynomial factors Solutions are also called roots Solutions are also called roots

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Zero Product Property Solve: Solve: (x – 3)(x + 6) = 0 (x – 3)(x + 6) = 0 x – 3 = 0 or x + 6 = 0 zero prod. Prop x – 3 = 0 or x + 6 = 0 zero prod. Prop x = 3 or x = -6 solve x = 3 or x = -6 solve

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Zero Product Property Solve: Solve: (4x + 5)(4x – 5) = 0 (4x + 5)(4x – 5) = 0 4x+5 = 0 or 4x – 5 =0 zero prod. prop 4x+5 = 0 or 4x – 5 =0 zero prod. prop 4x = -5 or 4x = 5 solve 4x = -5 or 4x = 5 solve x = -5/4 or x = 5/4 x = -5/4 or x = 5/4

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Solve by factoring Solve: 6x 2 + 12x = 0 Solve: 6x 2 + 12x = 0 6x (x + 2) = 0 factor 6x (x + 2) = 0 factor 6x = 0 or x + 2 = 0 zero prod. Prop 6x = 0 or x + 2 = 0 zero prod. Prop x = 0 or x = -2 solve x = 0 or x = -2 solve

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Solve by Factoring Solve: Solve: -10b 2 + 25b = 0 -10b 2 + 25b = 0 -5b (2b + 5) = 0 factor -5b (2b + 5) = 0 factor -5b = 0 or 2b + 5 = 0 zero prod. Prop -5b = 0 or 2b + 5 = 0 zero prod. Prop b = 0 or b = -5/2 b = 0 or b = -5/2

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Factor trinomials x 2 +bx+c Use guess and check Use guess and check Use x-factor Use x-factor

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Factor k 2 + 6k -7 k 2 + 6k -7 x factor x factor or guess and check or guess and check (x -1)(x +7) (x -1)(x +7) x – 1 = 0 x + 7 = 0 x – 1 = 0 x + 7 = 0 + 1 + 1 -7 -7 + 1 + 1 -7 -7 x = 1 x = -7 x = 1 x = -7 6 -7

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Factor d 2 + 5d – 50 d 2 + 5d – 50 x factor or guess and check x factor or guess and check (x + 10) or (x – 5 ) (x + 10) or (x – 5 ) x + 10 = 0 x – 5 = 0 x + 10 = 0 x – 5 = 0 -10 -10 +5 +5 -10 -10 +5 +5 x = -10 x = 5 x = -10 x = 5 5 -50

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Factor -2b 2 + 14b – 20 -2b 2 + 14b – 20 -2(b 2 – 7b + 10) Factor out -2 -2(b 2 – 7b + 10) Factor out -2 x factor or guess and check x factor or guess and check (x - 2) or (x – 5 ) (x - 2) or (x – 5 ) x - 2 = 0 x – 5 = 0 x - 2 = 0 x – 5 = 0 +2 +2 +5 +5 +2 +2 +5 +5 x = 2 x = 5 x = 2 x = 5 -7 10

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Solving Equations by Factoring Definition of Quadratic Equations Zero-Factor Property Strategy for Solving Quadratics.

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