Algebra 1

1
Algebra 1 Section 10.6 B Solving Quadratic
Equations by Factoring
Solve the equation by factoring.

• 2x2 9x 35 0

0
2x
x
5
- 7
factor into 2 binomials
2x 5 0 or x 7 0 set each factor
equal to 0

• 5 - 5
• 2x -5
• x -2 ½ or

7 7 x 7
2. 7x2 10x 3 0
0
x
- 1
7x
- 3
factor into 2 binomials
7x 3 0 or x 1 0 set each factor
equal to 0
3 3 7x 3 x 3/7 or
1 1 x 1
2
3. 3x2 34x 11 0
x
11
factor into 2 binomials
0
3x
1
3x 1 0 or x 11 0 set each
factor equal to 0
-11 -11 x - 11

• 1 - 1
• 3x -1
• x - 1/3 or

4. 5x2 3x 26 0
factor into 2 binomials
0
5x
x
- 13
2
5x 13 0 or x 2 0 set each factor
equal to 0
13 13 5x 13 x 13/5
-2 -2 x - 2
3 or 5
x 2
3
5. 4x2 21x 5 0
4x
x
- 1
- 5
0
factor into 2 binomials
4x 1 0 or x 5 0 set each factor
equal to 0
1 1 4x 1 x ¼ or
5 5 x 5
6. 2x2 17x 19 0
0
2x
x
- 19
1
factor into 2 binomials
2x 19 0 or x 1 0 set each factor
equal to 0
19 19 2x 19 x 19/2 x 9 ½ or
-1 -1 x -1
4
7. 6z2 z 70 0
0
3z
2z
- 10
7
factor into 2 binomials
3z 10 0 or 2z 7 0 set each factor
equal to 0
10 10 3z 10 z 10/3
-7 -7 2z -7 z -7/2 z -3 ½
1 or 3
z 3
8. 8y2 2y 3 0
0
4y
2y
3
- 1
factor into 2 binomials
4y 3 0 or 2y 1 0 set each factor
equal to 0

• 3 - 3
• 4y - 3
• y -3/4 or

1 1 2y 1 y ½