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] |

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|[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 |

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|[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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