Unit 9 Worksheet
Algebra 2
Unit 11.7
Factoring and Solving Trinomials (Quadratics) (a=1)
NOTES
[pic]
Steps to Factor Trinomials: Ex: [pic]
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
EXAMPLES
Factor and solve the following quadratics.
Factor Solve
1. [pic]
2. [pic]
3. [pic]
Factor out GCF. Then factor the remaining trinomial.
Factor Solve
4. [pic]
5. [pic]
Algebra 2 Name_______________________
11.7 Factoring and Solving Quadratic Period 1 2 3 4 5 6 7
Trinomials
ASSIGNMENT
|Factor and solve each quadratic. C and B Level |
| Factor: Solve: |
|1. [pic]= 0 |
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| Factor: Solve: |
|2. [pic]= 0 |
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| Factor: Solve: |
|3. [pic]= 0 |
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| Factor: Solve: |
|4. [pic]= 0 |
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| Factor: Solve: |
|5. [pic]= 0 |
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| Factor: Solve: |
|6. [pic]= 0 |
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| Factor: Solve: |
|7. [pic]= 0 |
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| Factor: Solve: |
|8. [pic]= 0 |
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| Factor: Solve: |
|9. [pic]= 0 |
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| Factor: Solve: |
|10. [pic]= 0 |
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|Factor out the GCF. Then factor the remaining quadratic and solve. A Level |
| Factor: Solve: |
|11. [pic]= 0 |
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| Factor: Solve: |
|12. [pic]= 0 |
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| Factor: Solve: |
|13. [pic] |
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| Factor: Solve: |
|14. [pic] |
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| Factor: Solve: |
|15. [pic] |
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| Factor: Solve: |
|16. [pic] |
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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 |19. Which binomial is one of |
|the factors of |the factors of |the factors of |
|[pic] |[pic] |[pic] |
| | | |
|[pic] |[pic] |[pic] |
|[pic] |[pic] |[pic] |
|[pic] |[pic] |[pic] |
|[pic] |[pic] |[pic] |
|Factor out the GCF from each polynomial. |
|20. [pic] |21. [pic] |22. [pic] |
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|23. [pic] is the greatest common factor (GCF) of |24. [pic] is the greatest common factor |
|which of the following? |(GCF) of which of the following |
| | |
|[pic]+ [pic] |[pic]+[pic] |
|[pic]+[pic] |[pic]+[pic] |
|[pic]+[pic] |[pic]+[pic] |
|[pic]+[pic] |[pic]+[pic] |
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PRACTICE TEST
|Level C |Level B |Level A |
|1C. Factor. |1B. Solve by factoring. |1A. Solve by factoring. |
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|[pic] |[pic] | [pic] |
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Answer Key
|1. (x-6)(x-5) |6. (x-4)(x+3) |11. 2(x2 +5x+6) |16. 2(x2 -8x+15) |21. [pic] |
|x=5,6 |x= -3,4 | 2(x+2)(x+3) | 2(x-3)(x-5) | |
| | | x= -3, -2 | x= 3, 5 | |
|2. (x-4)(x-5) |7. (x-20)(x-1) |12. 3(x2 +5x-6) |17. a |22. [pic] |
|x=4,5 |x=1,20 | 3(x-1)(x+6) | | |
| | | x= -6, 1 | | |
|3. (x+8)(x+8) |8. (x-5)(x+2) |13. 6(x2 -10x+9) |18. c |23. c |
|x= -8 |x= -2,5 | 6(x-9)(x-1) | | |
| | | x= 1,9 | | |
|4. (x+1)(x+1) |9. (x-7)(x-2) |14. 2(x2 +12x+20) |19. b |24. d |
|x= -1 |x=2,7 | 2(x+10)(x+2) | | |
| | | x= -10, -2 | | |
|5. (x-5)(x-1) |10. (x+3)(x-1) |15. 5(x2 -5x-24) |20. [pic] | |
|x=1,5 |x= -3,1 | 5(x+3)(x-8) | | |
| | | x= -3, 8 | | |
Practice Test Answers
|1C (x+7)(x+3) |1B x = -8, 4 |1A x = 3, 5 |
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