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Factoring by GCF Worksheet - Page 2

Factoring by GCF Worksheet
  • Page 2
 11.  
Factor:
8x3 - 1331
a.
(2x + 11) (4x2 - 22x + 121)
b.
(2x - 11) (4x2 + 22x + 121)
c.
(2x + 11) (121x2 + 22x + 4)
d.
(2x - 11)(2x + 11)


Solution:

8x3 - 1331

= (2x)3 - (11)3
[a = 2x, b = 11.]

= (2x - 11) [(2x)2 + (2x)(11) + (11)2]
[(a3 - b3) = (a - b) (a2 + ab + b2).]

= (2x - 11) (4x2 + 22x + 121)
[Simplify.]


Correct answer : (2)
 12.  
Factor:
1000x6 + 729y3
a.
(10x2 + 9y) (100x4 - 90x2y + 81y2)
b.
(100x6 + 81y2)
c.
(10x2 + 9y) (100x4 + 90x2y + 81y2)
d.
(10x2 + 9y) (100x4 + 81y2)


Solution:

1000x6 + 729y3

= (10x2)3 + (9y)3
[a = 10x2, b = 9y.]

= (10x2 + 9y) [(10x2)2 - (10x2) (9y) + (9y)2]
[(a3 + b3) = (a + b) (a2 - ab + b2).]

= (10x2 + 9y) (100x4 - 90x2y + 81y2)
[Simplify.]


Correct answer : (1)
 13.  
Factor:
x2 + 1 5x + 1100
a.
(x - 10)2
b.
(x + 10)2
c.
(x + 1 10)2
d.
(x - 1 10)2


Solution:

x2 + 1 / 5x + 1100

= (x2 + 1 / 5x + (1 / 10)2)

= [(x2 + 2(1 / 10)x + (1 / 10)2]
[a = x, b = 1 / 10.]

= (x + 1 / 10)2
[a2 + 2ab + b2 = (a + b)2.]


Correct answer : (3)
 14.  
Factor:
1 5x2 + 4 5x + 4 5
a.
5(x - 2)2
b.
5(x + 2)2
c.
15(x+2)2
d.
15(x-2)2


Solution:

1 / 5x2 + 4 / 5x + 4 / 5

= 15(x2 + 4x + 4)

= 15(x2+2(x)(2)+22)
[a = x, b = 2.]

= 1 / 5(x + 2)2
[a2 + 2ab + b2 = (a + b)2.]


Correct answer : (3)
 15.  
Factor:
5x3 - 1 25
a.
125(5x - 1)[25x2 + 5x + 1]
b.
25(5x + 1)[25x2 - 5x + 1]
c.
25(5x - 1)[25x2 - 5x + 1]
d.
125(5x + 1)[25x2 + 5x + 1]


Solution:

5x3 - 1 / 25

= 1 / 25(125x3 - 1)

= 1 / 25((5x)3 - 13)
[a = 5x, b = 1.]

= 125(5x - 1)[(5x)2+(5x)(1)+12)]
[(a3 - b3) = (a - b) (a2 + ab + b2).]

= 125(5x - 1)[25x2 + 5x + 1]
[Simplify.]


Correct answer : (1)
 16.  
Factor:
4x2 - 1 64
a.
64(16x + 1)(16x - 1)
b.
1 64(16x + 1)2
c.
1 64(16x + 1)(16x - 1)
d.
1 64(16x - 1)2


Solution:

4x2 - 1 / 64

= 164(256x2 - 1)

= 164[(16x)2 -12]
[a = 16x, b = 1.]

= 1 / 64(16x + 1)(16x - 1)
[a2 - b2 = (a + b) (a - b).]


Correct answer : (3)
 17.  
Factor:
0.25x2 - 0.1xy + 0.01y2
a.
1 0.01(5x - y)2
b.
1 0.01(5x + y)2
c.
0.01(5x - y)2
d.
0.01(5x + y)2


Solution:

0.25x2 - 0.1xy + 0.01y2

= 0.01[25x2 - 10xy + y2]

= 0.01[(5x)2 - 2(5x)(y) + (y)2]
[a = 5x, b = y.]

= 0.01(5x - y)2
[a2 - 2ab + b2 = (a - b) 2.]


Correct answer : (3)
 18.  
Factor:
(3x + 6y)2 - 25z2
a.
(3x + 6y + 5z)2
b.
(3x + 6y - 5z)2
c.
(3x + y + 25z) (3x + y - 25z)
d.
(3x + 6y + 5z) (3x + 6y - 5z)


Solution:

(3x + 6y)2 - 25z2

= (3x + 6y)2 - (5z)2
[a = 3x + 6y, b = 5z.]

= (3x + 6y + 5z) (3x + 6y - 5z)
[(a + b) (a - b).]


Correct answer : (4)
 19.  
Factor:
r2 - (7s + 3t)2
a.
(r - 7s - 3t)2
b.
(r + 7s + 3t) (r + 7s - 3t)
c.
(r + 7s + 3t) (r - 7s - 3t)
d.
(r + 7s + t) (r - 7s - t)


Solution:

r2 - (7s + 3t)2

= [r + (7s + 3t)] [r - (7s + 3t)]
[a2 - b2 = (a + b)(a - b).]

= (r + 7s + 3t) (r - 7s - 3t)


Correct answer : (3)
 20.  
Factor:
x6a - y6a

a.
IV
b.
II
c.
III
d.
I


Solution:

x6a - y6a

= (x3a)2 - (y3a)2
[Use power property, amn = (am)n.]

= (x3a + y3a)(x3a - y3a)
[(a2 - b2) = (a + b) (a - b).]

= [(xa)3 + (ya)3)] [(xa)3 - (ya)3)]
[Use power property, amn = (am)n.]

= [(xa+ya)(x2a-xaya+y2a)] [(xa-ya)(x2a+xaya+y2a)]
[a3 + b3 = (a + b) (a2 - ab + b2) and a3 - b3 = (a - b) (a2 + ab + b2).]

= (xa+ya)(xa-ya)(x2a-xaya+y2a) (x2a+xaya+y2a)


Correct answer : (4)

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