Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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FactoringMixedPractice
FactoringPatternsthatWeKnow:
DifferenceofSquares(DOS)
𝑎! − 𝑏 ! = (𝑎 + 𝑏)(𝑎 − 𝑏)
SumsandProducts(SAP)
𝑥 ! + 𝑎 + 𝑏 𝑥 + 𝑎𝑏 = (𝑥 + 𝑎)(𝑥 + 𝑏)
Non-MonicQuadratics
Usesplittingthemiddleterm.
Directions:
1. FactoroutanyGCF.
2. Ifpossible,useoneofthepatternstofactortheresultingexpression.
Example4:18𝑥 ! − 50𝑥
1. 𝑥 ! − 𝑥 − 42
2. 4𝑥 ! − 25
3. 6𝑥 ! + 𝑥 − 35
4. 5𝑦 ! − 125
5. 4𝑥 ! + 12𝑥 + 9
6. 𝑥 ! + 4𝑥 − 21
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Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
7. 5𝑥 ! − 33𝑥 + 18
8. 49𝑥 ! − 121
9. 12𝑥 ! − 7𝑥 − 10
10. 9𝑥 ! − 16
11. 4𝑥 ! + 20𝑥 + 25
12. 𝑥 ! − 5𝑥 + 6
13. 5𝑥 ! + 15𝑥 ! − 20𝑥
14. 4𝑥 ! + 18
15. 𝑥 ! − 12𝑥 + 36
16. 𝑥 ! − 3𝑥 + 54
17. 6𝑥 ! − 21
18. 3𝑥 ! + 31𝑥 + 56
19. 16𝑥 ! − 1
20. 3𝑥 ! − 12𝑥 ! − 45𝑥
21. 𝑥 ! + 8𝑥 + 15
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Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
22. 75𝑥 ! − 27𝑥
23. 3𝑥 ! − 12𝑥 ! − 36𝑥
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24. 𝑥 ! + 10𝑥 ! − 24𝑥
Directions:SolveeachproblemusingtheZeroProductPropertyandfactoring.
25. 𝑥 − 2 𝑥 + 3 = 0
26. 2𝑥 − 1 𝑥 + 2 = 0
27. 2𝑥 𝑥 − 3 𝑥 + 4 = 0
28. 𝑥 ! − 10𝑥 + 25 = 0
29. 𝑥 ! − 4𝑥 = 5
30. 𝑥 ! − 2 = −2𝑥 − 10
31. 𝑥 ! + 6𝑥 = −9
32. 𝑥 ! − 8𝑥 + 16 = 0
33. 𝑥 ! = 9
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