Unit 9 More with Quadratics—Factored Form Lesson 13 Exploring Factored Form 551 NAME: PERIOD: DATE: Homework Problem Set For each problem below, find the GCF of the expression, if one exists. Be careful, some expressions have no GCF. 1. 9x 2 2 81 → GCF: 2. 2 4x 2 1 x → GCF: 3. 45x 2 2 9→ GCF: 4. 2 31x 2 2 3x → GCF: 5. 27x 2 9 → GCF: 6. 9x 2 4 → GCF: 7. 2 14x 2 1 35 → GCF: 8. 2 2x 2 2 3x → GCF: 9. x 2 2 6x 1 12 → GCF: 10. 2 6x 2 2 6x 1 6 → GCF: 11. 16x 2 1 8x 2 24 → GCF: 12. 60x 2 2 10x 1 6 → GCF: 13. 8x 2 2 4xy 1 2xw → GCF: 14. ax 2 1 ax 2 a → GCF: 15. 6bx 2 2 2bx 1 8b → GCF: 91 2 9 C4x D 915 2 1 q x 9 2 9 5 2 I 99 x 94 31 3 913 1 9 4 X 9 NONE 31 3 3 1 X 3k 9 y 2 75 Gx 13 XI 6 12 NONE 6 8 2 642 1 1 82 7 3 2130 2 5 3 2x a 2b 2x 4x 2ytw a 2 l 2b 3 2 4
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NAME: PERIOD: DATE: Homework Problem Set...Homework Problem Set For each problem below, find the GCF of the expression, if one exists. Be careful, some expressions have no GCF. 1.
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Unit 9 More with Quadratics—Factored Form Lesson 13 Exploring Factored Form 551
NAME: PERIOD: DATE:
Homework Problem Set
For each problem below, find the GCF of the expression, if one exists. Be careful, some expressions have no GCF.
1. 9x2 2 81 →
GCF:
2. 2 4x2 1 x →
GCF:
3. 45x2 2 9→
GCF:
4. 2 31x2 2 3x →
GCF:
5. 27x 2 9 →
GCF:
6. 9x 2 4 →
GCF:
7. 2 14x2 1 35 →
GCF:
8. 2 2x2 2 3x →
GCF:
9. x2 2 6x 1 12 →
GCF:
10. 2 6x2 2 6x 1 6 →
GCF:
11. 16x2 1 8x 2 24 →
GCF:
12. 60x2 2 10x 1 6 →
GCF:
13. 8x2 2 4xy 1 2xw →
GCF:
14. ax2 1 ax 2 a →
GCF:
15. 6bx2 2 2bx 1 8b →
GCF:
91 2 9 C4x D 915 2 1q x 92 9 5 2 I
99 x 94
31 3 913 1 9 4X 9 NONE
31 3 3 1X 3k 9
y2 75 Gx13 XI 6 12
NONE
6 8 2642 1 1 8 2 7 3 2130 2 5 3
2x a 2b2x 4x 2ytw a 2 l 2b 3 2 4
552 Module 4 Quadratic Functions
Factor each equation in Problems 16–21. You may use either the algebra tile model or the generic rectangle.
16. y 5 x2 1 2x 1 1 17. y 5 x2 1 4x 1 4
18. y 5 x2 1 6x 1 5 19. y 5 x2 1 7x 1 10
20. y 5 x2 1 6x 1 9 21. y 5 x2 1 8x 1 16
MULTIPLY multiply
y CxHKxH y 2 Cxt2 4ADD add
T
Y Htt CxHstoaddto2x proof'dud
multiply multiply5 10
5 Gts GH y Cxt5Xxt2 µ6 yadd add
multiply multiply
g Gt3 Cxt33 3 Y kt4JCxt4 416 8add add
Unit 9 More with Quadratics—Factored Form Lesson 13 Exploring Factored Form 553
Factor each equation in Problems 22–27.
22. y 5 2x2 1 7x 1 3 23. y 5 3x2 1 4x 1 1
24. y 5 4x2 1 13x 1 10 25. y 5 5x2 1 14x 1 8
26. y 5 3x2 1 11x 1 6 27. y 5 2x2 1 11x 1 15
X 3 3X I
y 3xtDCxt3 y C3xtDCxH
4 5 5 4
28 10 410 8
y 4 5 4y 4 xt5 CXt2
3 2 2x I
3 9 6 3 6 15
y 3Cxt2Xxt3 y C2xtDCxt3
554 Module 4 Quadratic Functions
Factor each equation in Problems 28–33.
28. y 5 2x2 2 7x 1 3 29. y 5 3x2 2 14x 2 5
30. y 5 4x2 1 x 2 3 31. y 5 4x2 2 4x 2 3
32. y 5 6x2 1 x 2 1 33. y 5 8x2 2 10x 2 3
y C2x DAD y Cx 5 BAD
y CxH 4 3 y 2 3 C2xtD
y C3x DC2xH y C4x 1 2 3
Unit 9 More with Quadratics—Factored Form Lesson 13 Exploring Factored Form 555
Challenge Problems
34. Fill in the boxes with any numbers that make the equation true.
35. Fill in the blanks by finding the largest and smallest integers that will make the quadratic expression factorable.
36. An algebra tile model was started but not completed and it is missing some pieces. What trinomial could this be representing? What is it in factored form?
Hint what iseasiest to fill out What are thefactorsof 12
AnswerManypossibilities P 4,1 55,83
Hin owwouldyourepresentthisWheatmpatt Yreyouobservingformax'sminvaluesof c