To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)

Factoring Polynomials Word Problems

Factoring Polynomials Word Problems
  • Page 1
 1.  
Factor:
a(a - 8) - b(b - 8)
a.
(a - b)(a - 8)(b + 8)
b.
(a - b)(a + b - 8)
c.
(a - b)(a - 8)(b - 8)
d.
(a - b)(a - b - 16)


Solution:

a(a - 8) - b(b - 8)

= a2 - 8a - b2 + 8b

= a2 - b2 - 8a + 8b
[Group the terms.]

= (a - b)(a + b) - 8(a - b)

= (a - b)(a + b - 8)


Correct answer : (2)
 2.  
Factor:
x37 - 4 7x2 + 3x7
a.
x7(x + 2)(x - 2)
b.
x7(x - 2)(x - 2)
c.
x7(x + 1)(x - 3)
d.
x7(x - 1)(x - 3)


Solution:

x37 - 4 / 7x2 + 3x7

= x7 (x2 - 4x + 3)
[Use the GCF to factor.]

= x7(x2 - 3x - x + 3)

= x7 (x - 1)(x - 3)


Correct answer : (4)
 3.  
Factor 9x6a - 81y6b completely.
a.
9 (x3a - 3y3b) (x3a + 3y3b)
b.
9(x3a - 3y3b)2
c.
9(x3a + 3y3b)2
d.
9(x6a - 9y6b)


Solution:

9x6a - 81y6b

= 9(x6a - 9y6b)
[GCF is 9.]

= 9[(x3a)2 - (3y3b)2]
[Write as perfect squares.]

= 9(x3a - 3y3b) (x3a + 3y3b)
[a2 - b2 = (a + b)(a - b).]


Correct answer : (1)
 4.  
Factor:
2dx + 8d + 5bx + 20b
a.
(2dx + d)(bx + 5b)
b.
(2d + x) (5b + 4)
c.
(x + 5b) (2d + 4)
d.
(2d + 5b) (x + 4)


Solution:

2dx + 8d + 5bx + 20b

= (2dx + 8d ) + (5bx + 20b)
[Group terms.]

= 2d(x + 4) + 5b (x + 4)
[Factor.]

= (2d + 5b) (x + 4)
[Factor again.]


Correct answer : (4)
 5.  
Factor:
169a2 + 130ab + 78ca + 30cb + 25b2
a.
(13a + 5c) (13a - 5b - 6c)
b.
(13a + 5b + 6c)(6c + 5b)
c.
(13a + 5b) (13a + 5b + 6c)
d.
(13a - 5b) (13a + 5b + 6c)


Solution:

= (169a2 + 130ab + 25b2) + (78ca + 30cb)
169a2 + 130ab + 78ca + 30cb + 25b2
[Rearrange.]

= (13a + 5b)2 + 6c(13a + 5b)
[(a + b)2 = a2 + 2ab + b2]

= (13a + 5b)(13a + 5b) + 6c(13a + 5b)

= (13a + 5b) (13a + 5b + 6c)
[Factor again.]


Correct answer : (3)
 6.  
Factor:
2x3 - 128
a.
2(x - 4)(x2 + 4x + 16)
b.
(x + 2)(x2 - 4x)
c.
(x - 4)(x2 + 64)
d.
(x - 4)(2x2 + 4x + 16)


Solution:

= 2(x3 - 64)
2x3 - 128
[GCF is 2.]

= 2(x - 4)(x2 + 4x + 16)
[ a3 - b3 = (a - b) (a2 + ab + b2 ).]


Correct answer : (1)
 7.  
Factor:
25e2 - 30eg - 9g + 15e + 9g2
a.
(5e - 3g) (5e - 9g)
b.
(5e - 3g) (5e - 3g + 3)
c.
(5e + 3g) (5e - 3g)
d.
(5e - 3g) (5e - 9g + 3)


Solution:

25e2 - 30eg - 9g + 15e + 9g2

= (25e2 - 30eg + 9g2 ) + (- 9g + 15e)
[Rearrange.]

= (5e - 3g)2 + 3(5e - 3g)
[(a + b)2 = a2 + 2ab + b2.]

= (5e - 3g) (5e - 3g + 3)
[Factor.]


Correct answer : (2)
 8.  
Factor:
5x2 - 125y2
a.
(5x - 5y)(x - 25y)
b.
(x - 5y) (5x + y)
c.
(5x - y) (x + y)
d.
5(x - 5y) (x + 5y)


Solution:

= 5(x2 - 25y2 )
5x2 - 125y2
[GCF is 5.]

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


Correct answer : (4)
 9.  
Factor:
n3 + r3 + n2 - r2
a.
(n3 + r3)
b.
(n3 + r3)(n2 - r2)
c.
(n + r) (n2 - nr + n - r + r2)
d.
(n + r) (n2 - nr + r2)


Solution:

n3 + r3 + n2 - r2

= (n3 + r3) + (n2 - r2)
[Group terms.]

= (n + r) (n2 - nr + r2) + (n + r) (n - r)
[ a3 + b3= (a + b) (a2 - ab + b2) and (a2 - b2) = (a + b) (a - b)]

= (n + r) (n2 - nr + r2 + n - r)
[Factor again.]

= (n + r) (n2 - nr + n - r + r2)
[Arrange in descending order of exponents.]


Correct answer : (3)
 10.  
Factor:
c3 + c2 - 16c - 448
a.
(c3 - 8) (c2 + 448)
b.
(c - 8) (c2 + 9c + 56)
c.
(c - 8) (c2 + 8c + 64)
d.
(c3 + c2)(16c - 448)


Solution:

c3 + c2 - 16c - 448

= c3 + c2 - 16c - 512 + 64
[Replace - 448 as (- 512 + 64).]

= (c3 - 512) + (c2 - 16c + 64)
[Rearrange.]

= (c - 8) (c2 + 8c + 64) + (c - 8)2
(a3 - b3) = (a - b) (a2 + ab + b2) and (a - b)2 = a2 - 2ab + b2.]

= (c - 8) (c2 + 8c + 64 + c - 8)
[Factor again.]

= (c - 8) (c2 + 9c + 56)
[Simplify.]


Correct answer : (2)

*AP and SAT are registered trademarks of the College Board.