Algebra 2
Unit 11.7
Factoring and Solving Trinomials (Quadratics) (a=1)
NOTES
ax 2  bx c
Steps to Factor Trinomials:
Ex:
1. Identify a, b, and c
2. Find all factors with a product of “c”
3. Choose the pair from step 2 with a sum of “b”
4. Create 2 binomials ( )( ) and split up the x2
(x )(x )
5. Put the chosen factors from step 3 into the
binomials, one in each.
Ex: factors 2, -3
(x + 2)(x – 3)
6. Double check using FOIL
7. To solve: Create 2 equations by setting each
biniomial = 0.
Ex: x + 2 = 0 and x – 3 = 0
8. Solve to get 2 answers.
Ex: x + 2 = 0 and x – 3 = 0
x = -2
x = 3
Reference Glencoe Textbook: Page 485-492 Chapter 8-3
x2  9x  14
EXAMPLES
Factor and solve the following quadratics.
Factor
1.
x 2  9x  18
2.
x 2  25x  24
3.
x 2  11x  30
Solve
Factor out GCF. Then factor the remaining trinomial.
Factor
4.
2x2  40x  200
5.
5x 2  30x  45
Reference Glencoe Textbook: Page 485-492 Chapter 8-3
Solve
Algebra 2
11.7 Factoring and Solving Quadratic
Trinomials
ASSIGNMENT
Factor and solve each quadratic.
Factor:
2
x  11x  30 = 0
1.
2.
x  9x  20 = 0
3.
x  16x  64 = 0
4.
x  2x  1 = 0
5.
x  6x  5 = 0
Name_______________________
Period 1 2
3 4 5 6 7
C and B Level
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
2
2
2
2
Reference Glencoe Textbook: Page 485-492 Chapter 8-3
6.
x  x  12 = 0
7.
x  21x  20 = 0
8.
x  3x  10 = 0
9.
x  9x  14 = 0
10.
x  2x  3 = 0
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
2
2
2
2
2
Reference Glencoe Textbook: Page 485-492 Chapter 8-3
Factor out the GCF. Then factor the remaining quadratic and solve.
Factor:
Solve:
2
2x  10x  12 = 0
11.
12.
3x  15x  18 = 0
13.
8x  30x  54  2x  30x
14.
7x  24x  15  5x  25
15.
2x  12x  120  -3x  13x
16.
x  16x  24  x  6
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
Factor:
Solve:
2
2
2
2
2
2
2
2
2
Reference Glencoe Textbook: Page 485-492 Chapter 8-3
A Level
MIXED REVIEW
Answer the following multiple Choice Questions
***Hint Factor the polynomial first***
17. Which binomial is one of
18. Which binomial is one of
the factors of
the factors of
2
x  5x  6
x 2  9x  10
a. (x  3)
b. (x  3)
c. (x  6)
d. (x  1)
19. Which binomial is one of
the factors of
x 2  14x  40
a. (x  8)
a. (x  2)
b. (x  5)
c. (x  10)
b. (x  4)
c. (x  2)
d. (x  20)
d. (x  10)
Factor out the GCF from each polynomial.
20. x 2 y  x
21. 25x 5  5x 3  15x 2
23. 3x 2 y is the greatest common factor (GCF) of
which of the following?
a. 3x 3y 2 + 6xy 3
b. 9x 4 y + 2x 3 y 3
c. 9x 4 y + 12x 2 y 4
d. 3x 2 y 3 + 10x y 3
Reference Glencoe Textbook: Page 485-492 Chapter 8-3
22. 48x 2  16y 2  32xy
24. 5x 3 y is the greatest common factor
(GCF) of which of the following
a. 20x 3 y 2 + 15xy 3
b. 5x 4 y + x 3 y 3
c. 25x 4 y + 15x 2 y 4
d. 5x 6 y 3 + 10x 3 y
PRACTICE TEST
Level C
Level B
1C. Factor.
Level A
1B. Solve by factoring.
1A. Solve by factoring.
x2  4x  32  0
x2  10x  21
Answer Key
1. (x-6)(x-5)
x=5,6
6. (x-4)(x+3)
x= -3,4
2. (x-4)(x-5)
x=4,5
7. (x-20)(x-1)
x=1,20
3. (x+8)(x+8)
x= -8
8. (x-5)(x+2)
x= -2,5
4. (x+1)(x+1)
x= -1
9. (x-7)(x-2)
x=2,7
5. (x-5)(x-1)
x=1,5
10. (x+3)(x-1)
x= -3,1
Practice Test Answers
1C (x+7)(x+3)
1B
11. 2(x2 +5x+6)
2(x+2)(x+3)
x= -3, -2
12. 3(x2 +5x-6)
3(x-1)(x+6)
x= -6, 1
13. 6(x2 -10x+9)
6(x-9)(x-1)
x= 1,9
14. 2(x2 +12x+20)
2(x+10)(x+2)
x= -10, -2
15. 5(x2 -5x-24)
5(x+3)(x-8)
x= -3, 8
x = -8, 4
Reference Glencoe Textbook: Page 485-492 Chapter 8-3
3x2  24x  45  0
16. 2(x2 -8x+15)
2(x-3)(x-5)
x= 3, 5
17. a
21.
2
3
5x (5x  x  3)
22.
16(3x
2
18. c
23. c
19. b
24. d
20. x (xy  1)
1A x = 3, 5
2
 y  2xy)