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algebra1chapter6studyguide


Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
 
 
Factor the polynomial.
 

 1. 
chapter6studyguidea_files/i0030000.jpg
a.
2x(x2 + 2x + 4)
c.
x(2x2 + 4x + 8)
b.
2x(x + 2)(x + 4)
d.
2x3 + 4x2 + 8x
 

 2. 
40w11 + 16w6
a.
8w6(5w5 + 2)
c.
w6(40w5 + 16)
b.
8(5w11 + 2w6)
d.
8w5(5w6 + 2w)
 

 3. 
54c3d4 + 9c4d2
a.
9c3d2(d2 + 6c)
c.
9c4d2(d2 + 6)
b.
9c3d2(6d2 + c)
d.
9c4d2(6d2 + 1)
 

 4. 
Find the GCF of the terms of the polynomial.
8x6 + 32x3
a.
x3
b.
8x3
c.
8x3
d.
8x6
 
 
Complete.
 

 5. 
y2 + 15y + 56 = (y + 7)(y +chapter6studyguidea_files/i0080000.jpg)
a.
–8
b.
8
c.
–7
d.
7
 

 6. 
z2 + 9z – 90 = (z – 6)(z +chapter6studyguidea_files/i0090000.jpg)
a.
–9
c.
90
b.
15
d.
–15
 
 
Factor the expression.
 

 7. 
w2 + 18w + 77
a.
(w – 7)(w + 11)
c.
(w + 7)(w + 11)
b.
(w – 7)(w – 11)
d.
(w + 1)(w + 77)
 

 8. 
d2 + 10d + 9
a.
(d + 9)(d – 1)
c.
(d – 9)(d – 1)
b.
(d – 9)(d + 1)
d.
(d + 9)(d + 1)
 

 9. 
x2 – 10xy + 24y2
a.
(x + 6y)(x + 4y)
c.
(x + 2y)(x – 12y)
b.
(x – 2y)(x + 12y)
d.
(x – 6y)(x – 4y)
 

 10. 
x2 – x – 42
a.
(x – 7)(x + 6)
c.
(x + 7)(x – 6)
b.
(x + 7)(x + 6)
d.
(x – 7)(x – 6)
 

 11. 
6x2 + 5x + 1
a.
(3x – 1)(2x – 1)
c.
(3x – 1)(2x + 1)
b.
(3x + 1)(2x – 1)
d.
(3x + 1)(2x + 1)
 

 12. 
chapter6studyguidea_files/i0160000.jpg
a.
2(5x – 2)(2x + 3)
c.
(10x – 2)(4x + 3)
b.
2(5x + 2)(2x – 3)
d.
2(5x + 4)(2x – 3)
 

 13. 
16j2 + 24j + 9
a.
(4j – 9)(4j + 1)
c.
(4j + 3)(4j – 3)
b.
(4j + 3)2
d.
(4j – 3)2
 

 14. 
16m2 – 24mn + 9n2
a.
(4m – 3n)(4m + 3n)
c.
(4m – 3n)2
b.
(16m – 3n)(m + 3n)
d.
(4m + 3n)2
 

 15. 
chapter6studyguidea_files/i0190000.jpg
a.
chapter6studyguidea_files/i0190001.jpg
c.
chapter6studyguidea_files/i0190002.jpg
b.
chapter6studyguidea_files/i0190003.jpg
d.
chapter6studyguidea_files/i0190004.jpg
 

 16. 
chapter6studyguidea_files/i0200000.jpg
a.
chapter6studyguidea_files/i0200001.jpg
b.
chapter6studyguidea_files/i0200002.jpg
c.
chapter6studyguidea_files/i0200003.jpg
d.
chapter6studyguidea_files/i0200004.jpg
 

 17. 
r2 – 49
a.
(r – 7)(r + 7)
c.
(r – 7)(r – 7)
b.
(r + 7)(r + 7)
d.
(r – 7)(r + 9)
 

 18. 
49b2 – 36
a.
(6b + 7)(6b – 7)
c.
(7b + 6)(7b – 6)
b.
(7b + 6)(7b + 6)
d.
(7b – 6)(7b – 6)
 

 19. 
3x3 + 3x2 + x + 1
a.
x(3x2 + x + 1)
c.
3x2(x + 1)
b.
(x + 3)(3x2 – 1)
d.
(x + 1)(3x2 + 1)
 

 20. 
Find the GCF of the first two terms and the GCF of the last two terms of the polynomial.
5h3 + 20h2 + 4h + 16
a.
5h2, 16
b.
5h3, 4
c.
5h2, 4
d.
h2, h
 

 21. 
Factor completely.
6x4 – 9x3 – 36x2 + 54x
a.
3x(x2 – 6)(2x – 3)
c.
6x(x2 – 6)(2x – 3)
b.
3x(x2 + 6)(2x + 3)
d.
6x(x2 + 6)(2x + 3)
 
 
Factor by grouping.
 

 22. 
21m2 – 29m – 10
a.
(7m – 2)(3m – 5)
c.
(7m + 2)(3m – 5)
b.
(7m + 2)(3m + 5)
d.
(7m – 2)(3m + 5)
 

 23. 
a2 + ab – 56b2
a.
(a + 8b)(a + 7b)
c.
(a + 8b)(a – 7b)
b.
(a – 8)(a + 7b)
d.
(a – 8b)(a – 7b)
 

 24. 
40p2 – 13p – 36
a.
(8p + 9)(5p + 4)
c.
(8p – 9)(5p + 4)
b.
(8p – 9)(5p – 4)
d.
(8p + 9)(5p – 4)
 

Short Answer
 

 25. 
Factor the following expression.
198q3r2 – 184q2r2 + 18qr2
 



 
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