10.4 Solving Factored Polynomial Equations

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Presentation transcript:

10.4 Solving Factored Polynomial Equations Find the value of x, Discuss as team why/how you determined the solution. 3(0) = x (0)(-5) = x (x)(7) = 0 -3x = 0 x = 0 x = 0 x = 0 x = 0 Zero Product Property If a · b = 0, then either a = 0 or b = 0.

10.4 Solving Factored Polynomial Equations As a team, Discuss the possible solutions for each of the following equations, EXPLAIN your reasoning: 1. 3x = 0 2. 5(x – 2) = 0 3. xy = 0 4. (x + 2)(x + 7) = 0

(x + 2)(x + 7) = 0 x + 2 = 0 or x + 7 = 0 x + 2 – 2 = 0 – 2 x = -2 x + 7 – 7 = 0 – 7 x = -7 {-2, -7}

Solve. (2x – 6)(3x + 5) = 0 2x – 6 = 0 or 3x + 5 = 0 x = 3

(x + 8)2 = 0 (x + 8)(x + 8) = 0 x + 8 = 0 x + 8 – 8 = 0 – 8 x = -8

(3x – 2)(4x + 3)(x + 4) = 0 3x – 2 = 0 or 4x + 3 = 0 or x + 4 =0

10.4 Solving Factored Polynomial Equations a quadratic equation in standard form. 2x2 – 7x + 15 = 0 a quadratic equation in factored form. (2x + 5)(x – 3) = 0 a polynomial equation in factored form. (2x + 5)(x – 3)(x + 7) = 0

Homework p. 600, #20-42 evens

10.4 Solving Factored Polynomial Equations Review: Linear, Quadratic Quadratic Equation : a polynomial equation with a degree of two Ex. x2 + 2x - 8 = -3 Factored Form of a Quadratic Equation: Equation in which the polynomial is written as the product of two linear expressions Ex. (x + 4)(x – 2) = -3