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Algebra 2
Unit 11.6
Solve an Equation by Factoring out the Greatest Common Factor
NOTES
Examples
Steps to solving an equation by taking factoring out the GCF.
1.
2.
3.
4.
Write the equation in standard form
Find the GCF.
Factor the GCF out of the quadratic.
Set each factors equal to zero and solve.
Factor and solve the equation.
Factor
Solve
a. 3x – 6 = 0
b. 2x + 10 = 0
c.
3x2 – 6x = 0
d. 15x2 + 6x = 0
e.
-4x2 = 12x
Reference Glencoe Textbook: Page 471-482 Chapter 8-1, 8-2
Algebra 2
Unit 11.6
Solve an Equation by Factoring out
the Greatest Common Factor
Name_______________________
Period 1 2 3 4 5 6 7
Factor and solve each equation.
1.
2.
3.
4.
5.
2x  4  0
18x  9  0
x 2  3x  0
2
C Level
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
12x  24x  0
3x 2  3x  0
Reference Glencoe Textbook: Page 471-482 Chapter 8-1, 8-2
Factor and solve each quadratic equation.
Factor:
6.
7.
8.
9.
10.
12x 2  8x  0
18x 2  9x  0
2
B Level
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
3x  x  0
24x 2  12x  0
27x 2  18x  0
Reference Glencoe Textbook: Page 471-482 Chapter 8-1, 8-2
Factor and solve each quadratic equation.
Factor:
11.
12.
13.
14.
15.
a 2  5a
2x
2
9x
2
A Level
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
 6x
 3x
20x 2  5x
6x 2  8x
Reference Glencoe Textbook: Page 471-482 Chapter 8-1, 8-2
PRACTICE TEST
Level C
1C. Solve.
3x2 – 18x = 0
Level B
1B. Solve.
14x2+ 21x = 0
Level A
1A. Solve.
15x2 = 5x
RANDOM ANSWERS
2x(x-3) = 0
x = 0, 3
9(2x-1) = 0
x=½
12x(2x+1) = 0
x = 0, -1/2
12x(x+2) = 0
x = 0, -2
3x(x-1) = 0
x = 0, 1
a(a+5) = 0
a = 0, -5
3x(3x+1) = 0
x = 0, -1/3
x(3x+1) = 0
x = 0, -1/3
x(x+3) = 0
x = 0, -3
9x(3x-2) = 0
x = 0, 2/3
2(x-2) = 0
x=2
2x(3x-4) = 0
x = 0, 4/3
Reference Glencoe Textbook: Page 471-482 Chapter 8-1, 8-2
5x(4x+1) = 0
x = 0, -1/4
9x(2x-1) = 0
x = 0, ½
4x(2x-2) = 0
x = 0, 2/3
1C.
3x(x-6) = 0
x = 0, 6
1B
7x(2x+3)=0
x = 0, -3/2
1A
5x(3x-1) = 0
x = 0, 1/3