Example 1A

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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
Substitute each solution for x into the original
equation.
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Example 1B
Solve each equation. Check your answer.
x(x 2) 0
Set each factor 0
x(x 2) 0
x 0 or x 2 0
Solve the second equation.
x 2
The solutions are 0 and 2.
Substitute each solution for x into the original
equation.
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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.
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
Solve each equation.
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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 6 or x 6
Solve each equation.
Both factors result in the same solution, so
there is one solution, 6.
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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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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
Factor the trinomial.
(x 3)(x 3) 0
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.
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
Solve each equation.
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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
1, 7
5. 2x2 12x 14 0
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6. x2 18x 81 0