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Factoring Polynomials Word Problems - Page 2

Factoring Polynomials Word Problems
  • Page 2
 11.  
Factor:
64x3+ y2- y3-16x2
a.
(4x -  y) (16x2 + x + y + y2)
b.
(64x3 +  y2)y3
c.
(4x -  y) (16x2 + 4xy - 4x -  y +  y2)
d.
(4x -  y) (16x2 +  y2)


Solution:

64x3+ y2- y3-16x2

= (64x3- y3) - (16x2- y2)
[Rearrange.]

= (4x -  y) (16x2 + 4xy +  y2) - (4x +  y) (4x -  y)
[a3-b3 = (a - b) (a2+ab+b2) and (a2-b2) = (a + b) (a - b).]

= (4x -  y) (16x2 + 4xy +  y2 - 4x -  y )
[Factor again.]

= (4x -  y) (16x2 + 4xy - 4x -  y +  y2)
[Arrange in descending order of exponents.]


Correct answer : (3)
 12.  
Factor:
25x2 + 40xy - 81z2 + 16y2
a.
(5x + 4y) (5x + 4y + 9z)
b.
(5x + 4y - 9z) (5x + 4y + 9z)
c.
(5x + 4y - 9z) (5x + 4y)
d.
(25x2 - 4xy ) (5z2 + 16y2)


Solution:

25x2 + 40xy - 81z2 + 16y2

= (25x2 + 40xy + 16y2) - 81z2
[Rearrange.]

= (5x + 4y)2 - 81z2
[(a + b)2 = a2 + 2ab + b2.]

= (5x + 4y - 9z) (5x + 4y + 9z)
[(a2 - b2) = (a + b) (a - b)]


Correct answer : (2)
 13.  
Factor:
- x2 - 15x + 34
a.
- (x - 2)(x + 17)
b.
(x - 2)(x + 17)
c.
- (x + 2)(x - 3)
d.
- (x - 2)(x - 34)


Solution:

- x2 - 15x + 34

= - (x2 + 15x - 34)
[Factor out the GCF - 1.]

= - (x2 + 17x - 2x - 34)

= - [x(x + 17) - 2(x + 17)]

= - (x - 2)(x + 17)


Correct answer : (1)
 14.  
Factor:
- 16x4 + 105x2 - 125
a.
(5 - x2) (4x - 5) (4x + 5)
b.
(x - 5)(x + 5) (5x - 4) (5x + 4)
c.
(5x2 - 4) (5x2 + 4)
d.
(5 - x2) (x - 5) (5x - 4)


Solution:

- 16x4 + 105 x2 - 125

= - (16x4 - 105 x2 + 125)
[Multiply through out by - 1.]

= - (16x4 - 80 x2 - 25x2 + 125)
[Express - 105x2 as - 80x2 - 25x2.]

= - [16x2 (x2 - 5) - 25(x2 - 5)]
[Factor.]

= - (16x2 - 25) (x2 - 5)
[Factor again.]

= (5 - x2) (4x - 5) (4x + 5)
[(a2 - b2) = (a + b) (a - b)]


Correct answer : (1)
 15.  
Factor:
36w2 - 24w - 16z2 + 4
a.
(6w + 4z - 2) (6w - 4z - 2)
b.
(36w2 - 24w)(16z2 + 2)
c.
(6w + 2) (6w - 4z - 2)
d.
(36w + 4z - 2) (w - 4z)


Solution:

36w2 - 24w - 16z2 + 4

= (36w2 - 24w + 4) - 16z2
[Rearrange.]

= (6w - 2)2 - (4z)2
[(a - b)2 = a2 - 2ab + b2]

= (6w - 2 + 4z) (6w - 2 - 4z)
[(a2 - b2) = (a + b) (a - b)]

= (6w + 4z - 2) (6w - 4z - 2)


Correct answer : (1)
 16.  
Factor completely.
343q2 l2 - 63q2
a.
(7l + 3) (49q2 l - 21)
b.
49q2 (7l + 3)
c.
7q2 (7l + 3) (7l - 3)
d.
(7ql + 3) (49ql - 21q2)


Solution:

343q2 l2 - 63q2

= 7q2 (49l2 - 9)
[GCF is 7q2.]

= 7q2 (7l + 3) (7l - 3)
[(a2 - b2) = (a + b) (a - b).]


Correct answer : (3)
 17.  
Factor completely.
343pm2 - 784pm + 448p
a.
7m(p - 7)2
b.
7p(7m - 8)2
c.
p(7m - 7)2
d.
7m(7m - 8)(7m + 8)


Solution:

343pm2 - 784pm + 448p

= 7p(49m2 - 112m + 64)
[GCF is 7p.]

= 7p(7m - 8)2
[(a - b)2= a2 - 2ab + b2.]


Correct answer : (2)
 18.  
Factor:
6b2 + 12b - 48
a.
6(b + 8)(b - 4)
b.
(6b + 2)(b - 8)
c.
6(b - 2)(b + 4)
d.
- 12(b + 2)(b + 4)


Solution:

6b2 + 12b - 48

= 6(b2 + 2b - 8)
[Use the GCF to factor.]

= 6(b2 + 4b - 2b - 8)

= 6[b(b + 4) - 2(b + 4)]

= 6(b - 2)(b + 4)


Correct answer : (3)
 19.  
Factor completely.
44x4 - 1529x2 - 1980
a.
11x (4x2 + 144x + 36)
b.
11(4x2 + 5) (x2 - 144)
c.
11(x2 + 5) (4x + 6) (x - 6)
d.
11(4x2 + 5) (x + 6) (x - 6)


Solution:

= 11(4x4 - 139x2 - 180)
44x4 - 1529x2 - 1980
[GCF is 11.]

= 11(4x4 - 144x2 + 5x2 - 180)
[Express - 139x2 as - 144x2 + 5x2.]

= 11[4x2 (x2 - 36) + 5(x2 - 36)]
[Factor.]

= 11(4x2 + 5) (x2 - 36)
[Factor again.]

= 11(4x2 + 5) (x + 6) (x - 6)
[(a2 - b2) = (a + b) (a - b)]


Correct answer : (4)
 20.  
Factor:
17k3 - 3m3 + 3k2 m - 17km2
a.
(17k + 3m) (k + m) (k - m)
b.
(17k + 3m) (k2 + 17m)
c.
(17k + m) (k + 3m) (k - m)
d.
(17k - 3m) (k - m)


Solution:

17k3 - 3m3 + 3k2 m - 17km2

= (17k3 + 3k2m) + (- 3m3 - 17km2 )
[Rearrange and group the terms.]

= k2 (17k + 3m) - m2 (3m + 17k)
[Factor .]

= (k2- m2) (17k + 3m)
[Factor again.]

= (17k + 3m) (k + m) (k - m)
[(a2 - b2) = (a + b) (a - b)]


Correct answer : (1)

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