Solve quadratic equations by factoring.

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Objective
Solve quadratic equations by factoring.
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You have solved quadratic equations by graphing.
Another method used to solve quadratic equations
is to factor and use the Zero Product Property.
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Example 1A Use the Zero Product Property
Use the Zero Product Property to solve the
equation. Check your answer.
(x 7)(x 2) 0
Use the Zero Product Property.
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
Use the Zero Product Property to solve the
equation. Check your answer.
Substitute each solution for x into the original
equation.
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Example 1B Use the Zero Product Property
Use the Zero Product Property to solve each
equation. Check your answer.
(x 2)(x) 0
Use the Zero Product Property.
(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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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 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
Use the Zero Product Property.
Solve each equation.
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Example 2B Solving Quadratic Equations by
Factoring
Solve the quadratic equation by factoring. Check
your answer.
x2 4x 21
The equation must be written in standard form. So
subtract 21 from both sides.
(x 7)(x 3) 0
Factor the trinomial.
x 7 0 or x 3 0
Use the Zero Product Property.
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
Use the Zero Product Property.
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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Example 2C Continued
Solve the quadratic equation by factoring. Check
your answer.
x2 12x 36 0
Check Graph the related quadratic function.
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Example 2D Solving Quadratic Equations by
Factoring
Solve the quadratic equation by factoring. Check
your answer.
2x2 20x 50
The equation must be written in standard form. So
add 2x2 to both sides.
2x2 20x 50 0
Factor out the GCF 2.
2(x2 10x 25) 0
Factor the trinomial.
2(x 5)(x 5) 0
2 ? 0 or x 5 0
Use the Zero Product Property.
x 5
Solve the equation.
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Example 2D Continued
Solve the quadratic equation by factoring. Check
your answer.
2x2 20x 50
Check
Substitute 5 into the original equation.
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Example 3 Application
The height in feet of a diver above the water can
be modeled by h(t) 16t2 8t 8, where t is
time in seconds after the diver jumps off a
platform. Find the time it takes for the diver to
reach the water.
h 16t2 8t 8
The diver reaches the water when h 0.
0 16t2 8t 8
0 8(2t2 t 1)
Factor out the GFC, 8.
0 8(2t 1)(t 1)
Factor the trinomial.
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Example 3 Continued
Use the Zero Product Property.
8 ? 0, 2t 1 0 or t 1 0
2t 1 or t 1
Solve each equation.
It takes the diver 1 second to reach the water.
Check 0 16t2 8t 8
Substitute 1 into the original equation.
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