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Published byAdrian Willis Modified over 7 years ago

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Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0 Set each factor = 0 x – 7 = 0 or x + 2 = 0 Solve each equation. x = 7 or x = –2 The solutions are 7 and –2.

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** Example 1A Continued (7 – 7)(7 + 2) 0 (0)(9) 0**

Check (x – 7)(x + 2) = 0 (7 – 7)(7 + 2) 0 (0)(9) 0 0 0 Substitute each solution for x into the original equation. Check (x – 7)(x + 2) = 0 (–2 – 7)(–2 + 2) 0 (–9)(0) 0 0 0

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**Substitute each solution for x into the original equation.**

Example 1B Solve each equation. Check your answer. x(x – 2) = 0 x(x – 2) = 0 Set each factor = 0 x = 0 or x – 2 = 0 Solve the second equation. x = 2 The solutions are 0 and 2. (x – 2)(x) = 0 (2 – 2)(2) 0 (0)(2) 0 Check (x – 2)(x) = 0 (0 – 2)(0) 0 (–2)(0) 0 Substitute each solution for x into the original equation.

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**Substitute each solution for x into the original equation.**

Check It Out! Example 1a Solve each equation. Check your answer. x(x + 4) = 0 Set each factor = 0 x = 0 or x + 4 = 0 Solve the second equation. x = –4 The solutions are 0 and –4. Check (x)(x + 4) = 0 (0)(0 + 4) 0 (0)(4) 0 0 0 (x)(x +4) = 0 (–4)(–4 + 4) 0 (–4)(0) 0 Substitute each solution for x into the original equation.

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Check It Out! Example 1b Solve the equation. Check your answer. (3x + 4)(5x – 3) = 0 Set each factor = 0 3x + 4 = 0 or 5x – 3 = 0 Solve each equation.

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If a quadratic equation is written in standard form, ax2 + bx + c = 0, then to solve the equation, you may need to factor before using the Zero Product Property.

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**Example 2A: Finding Zeros by Factoring**

Find the zeros of the function by factoring. f(x) = x2 – 4x – 12 x2 – 4x – 12 = 0 Set the function equal to 0. (x + 2)(x – 6) = 0 Factor: Find factors of –12 that add to –4. x + 2 = 0 or x – 6 = 0 Set factors = 0 x= –2 or x = 6 Solve each equation.

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**Example 2A: Solving Quadratic Equations by Factoring**

Solve the quadratic equation by factoring. Check your answer. x2 – 6x + 8 = 0 (x – 4)(x – 2) = 0 Factor the trinomial. x – 4 = 0 or x – 2 = 0 Set each factor = 0 x = 4 or x = 2 The solutions are 4 and 2. Solve each equation. x2 – 6x + 8 = 0 (4)2 – 6(4) 16 – 0 0 Check x2 – 6x + 8 = 0 (2)2 – 6(2) 4 – 0 0 Check

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**Example 2C: Solving Quadratic Equations by Factoring**

Solve the quadratic equation by factoring. Check your answer. x2 – 12x + 36 = 0 (x – 6)(x – 6) = 0 Factor the trinomial. x – 6 = 0 or x – 6 = 0 x = or x = 6 Solve each equation. Both factors result in the same solution, so there is one solution, 6.

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**Find the zeros of the function by factoring.**

Check It Out! Example 2a Find the zeros of the function by factoring. f(x)= x2 – 5x – 6 x2 – 5x – 6 = 0 Set the function equal to 0. (x + 1)(x – 6) = 0 Factor: Find factors of –6 that add to –5. x + 1 = 0 or x – 6 = 0 x = –1 or x = 6 Solve each equation.

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**Find the zeros of the function by factoring.**

Check It Out! Example 2b Find the zeros of the function by factoring. g(x) = x2 – 8x x2 – 8x = 0 Set the function to equal to 0. Factor: Need factors of 0 that add to -8 x(x – 8) = 0 x = 0 or x – 8 = 0 x = 0 or x = 8 Solve each equation.

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**Example 2B: Finding Zeros by Factoring**

Find the zeros of the function by factoring. g(x) = 3x2 + 18x 3x2 + 18x = 0 Set the function to equal to 0. Factor: Divide by 3, then find factors of 0 that add to 6 3x = 0 or x + 6 = 0 x = 0 or x = –6 Solve each equation.

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Check It Out! Example 2a Solve the quadratic equation by factoring. Check your answer. x2 – 6x + 9 = 0 (x – 3)(x – 3) = 0 Factor the trinomial. x – 3 = 0 or x – 3 = 0 x = 3 or x = 3 Solve each equation. Both equations result in the same solution, so there is one solution, 3. x2 – 6x + 9 = 0 (3)2 – 6(3) 9 – 0 0 Check Substitute 3 into the original equation.

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Check It Out! Example 2d Solve the quadratic equation by factoring. Check your answer. 3x2 – 4x + 1 = 0 (3x – 1)(x – 1) = 0 Factor the trinomial. 3x – 1 = 0 or x – 1 = 0 or x = 1 Solve each equation. The solutions are and x = 1.

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Lesson Quiz: Part I Solve each equation. Check your answers. 1. (x – 10)(x + 5) = 0 2. (x + 5)(x) = 0 Solve each quadratic equation by factoring. Check your answer. 3. x2 + 16x + 48 = 0 10, –5 –5, 0 –4, –12

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Lesson Quiz: Part II 5. 2x2 + 12x – 14 = 0 1, –7 6. x2 + 18x + 81 = 0 –9

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