Solving Quadratic Equations
9-6 by Factoring
Warm Up
Find each product.
1. (x + 2)(x + 7)
2. (x – 11)(x + 5)
3. (x – 10)2
Factor each polynomial.
4. x2 + 12x + 35
5. x2 + 2x – 63
6. x2 – 10x + 16
7. 2x2 – 16x + 32
Solving Quadratic Equations
9-6 by Factoring
Learning Goals
1.  Students will use the Zero Product
Property to solve quadratic equations
2.  Students will solve quadratic equations
by factoring
Solving Quadratic Equations
9-6 by Factoring
You have solved quadratic equations by graphing.
Another method used to solve quadratic equations is to
factor and use the Zero Product Property.
Solving Quadratic Equations
9-6 by Factoring
Example 1: Use the Zero Product Property
Use the Zero Product Property to solve the
equation. Check your answer.
x2 – 5x - 14 = 0
x2 – 2x = 0
A. (x – 7)(x + 2) = 0
B. (x – 2)(x) = 0
x2 + 4x = 0
C. (x)(x + 4) = 0
x2 + x - 12 = 0
D. (x + 4)(x – 3) = 0
Solving Quadratic Equations
9-6 by Factoring
Example 1: Use the Zero Product Property
Use the Zero Product Property to solve the
equation. Check your answer.
x2 – 6x - 16 = 0
x2 – 11x - 30 = 0
a. (x + 2)(x - 8) = 0
b. (x – 6)(x - 5) = 0
x2 + 16x + 63 = 0
c. (x + 7)(x + 9) = 0
x2 - x = 0
d. (x)(x – 1) = 0
Solving Quadratic Equations
9-6 by Factoring
Example 1: Use the Zero Product Property
Use the Zero Product Property to solve the
equation. Check your answer.
x2 + 11x = 0
12x2 + 5x - 2 = 0
e. (x)(x + 11) = 0
f. (3x + 2)(4x - 1) = 0
6x2 + 11x - 35 = 0
g. (2x + 7)(3x - 5) = 0
5x2 - 17x - 12 = 0
h. (x - 4)(5x + 3) = 0
Solving Quadratic Equations
9-6 by Factoring
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.
Helpful Hint
To review factoring techniques, see lessons 8-3
through 8-5.
Solving Quadratic Equations
9-6 by Factoring
Example 2: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
A. x2 – 6x + 8 = 0
B. x2 + 4x = 21
C. x2 – 12x + 36 = 0
D. –2x2 = 20x + 50
E. x2 + 4x = 0
F. x2 - x = 0
Solving Quadratic Equations
9-6 by Factoring
Example 2: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
a. 3x2 – 4x + 1 = 0
b. 30x = –9x2 – 25
c. x2 + 4x = 5
d. x2 – 6x + 9 = 0
Solving Quadratic Equations
9-6 by Factoring
Example 2: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
e. x2 + 4x - 12 = 0
f.
g. x2 + 5x + 6 = 0
h. x2 – 3x = 10
x2 – 8x – 9 = 0
Solving Quadratic Equations
9-6 by Factoring
Example 2: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
i. x2 + 10x = -16
j.
k. x2 - 8x + 16 = 0
l. -3x2 = 18x + 27
x2 + 2x = 15
Solving Quadratic Equations
9-6 by Factoring
Example 2: Solving Quadratic Equations by Factoring
Solve the quadratic equation by factoring. Check
your answer.
i. x2 + 36 = 12x
Solving Quadratic Equations
9-6 by Factoring
Helpful Hint
(x – 3)(x – 3) is a perfect square. Since both
factors are the same, you solve only one of them.
Solving Quadratic Equations
9-6 by Factoring
Example 3: Application
A) 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.
Solving Quadratic Equations
9-6 by Factoring
Check It Out! Example 3
a)  The equation for the height above the water for
another diver can be modeled by
h = –16t2 + 8t + 24. Find the time it takes this diver
to reach the water.
Solving Quadratic Equations
9-6 by Factoring
Check It Out! Example 3
a)  The equation for the height above the water for
another diver can be modeled by
h = –16t2 + 8t + 24. Find the time it takes this diver
to reach the water.
Solving Quadratic Equations
9-6 by Factoring
Lesson Quiz: Part I
Use the Zero Product Property to 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
4. x2 – 11x = –24
• 
Solving Quadratic Equations
9-6 by Factoring
Lesson Quiz: Part II
5. 2x2 + 12x – 14 = 0
6. x2 + 18x + 81 = 0
7. –4x2 = 16x + 16
8. The height of a rocket launched upward from
a 160 foot cliff is modeled by the function
h(t) = –16t2 + 48t + 160, where h is height
in feet and t is time in seconds. Find the
time it takes the rocket to reach the ground
at the bottom of the cliff.