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Factoring Polynomials Word Problems - Page 3

Factoring Polynomials Word Problems
  • Page 3
 21.  
Factor:
c5 - 36c3 + 8c2 - 288
a.
(c + 2) (c2 - 2c + 4) (c2 - 6)
b.
(c + 2) (c2 - 2c + 4) (c - 6) (c + 6)
c.
(c + 2) (c2 - 2c + 2) (c - 2) (c + 2)
d.
(c - 2) (c2 + 2c + 36) (c - 6)


Solution:

c5 - 36c3 + 8c2 - 288

= c3 (c2 - 36) + 8(c2 - 36)
[Factor.]

= (c3 + 8) (c2 - 36)
[Factor again.]

= (c + 2) (c2 - 2c + 4) (c - 6) (c + 6)
[ a3 + b3= (a + b) (a2 - ab + b2) and (a2 - b2) = (a + b) (a - b)]


Correct answer : (2)
 22.  
Factor:
0.3x2 - 3.6x + 9.6
a.
1.2(x - 4)(x - 4)
b.
(0.3x - 4)(x - 8)
c.
0.3(x - 4)(x - 8)
d.
(x - 0.3)(x - 1.3)


Solution:

0.3x2 - 3.6x + 9.6

= 0.3(x2 - 12x + 32)
[Use the GCF to factor.]

= 0.3(x2 - 8x - 4x + 32)

= 0.3[x(x - 8) - 4(x - 8)]

= 0.3(x - 4)(x - 8)


Correct answer : (3)
 23.  
Factor:
9ax3 - 243a + 10bx3 - 270b
a.
(9ax + 10b) (x - 3) (x + 3)
b.
(9a + 10b) (x - 3) (x2 + 3x + 9)
c.
(a + b) (x - 3) (x2 + 3)
d.
ab(x3 - 1)2


Solution:

9ax3 - 243a + 10bx3 - 270b

= 9a (x3 - 27) + 10b (x3 - 27)
[Factor.]

= (9a + 10b) (x3 - 27)
[Factor again.]

= (9a + 10b) (x - 3) (x2 + 3x + 9)
[ a3 - b3 = (a - b) (a2 + ab + b2)]


Correct answer : (2)
 24.  
Factor:
b4 - 625
a.
(b2 + 4) (x - 25) (x + 25)
b.
(b2 + 5) (b - 5) (b + 5)
c.
(b2 + 25) (b - 5) (b + 5)
d.
(b2 + 625) (b - 4) (b + 4)


Solution:

b4 - 625

= (b2 + 25) (b2 - 25)
[(a2 - b2) = (a + b) (a - b)]

= (b2 + 25) (b - 5) (b + 5)
[(a2 - b2) = (a + b) (a - b)]


Correct answer : (3)
 25.  
Factor:
b16 - 16
a.
(b8 + 4) (b4 - 2) (b4 + 2)
b.
(b8 - 2) (b8 + 8)
c.
(b8 + 4) (b8 - 2)
d.
(b8 + 2) (b4 - 4) (b4 + 2)


Solution:

b16 - 16

= (b8 + 4) (b8 - 4)
[(a2 - b2) = (a + b) (a - b).]

= (b8 + 4) (b4 - 2) (b4 + 2)
[(a2 - b2) = (a + b) (a - b).]


Correct answer : (1)
 26.  
Factor:
20x2 - 49xy + 30y2
a.
(x - 5)2
b.
(x - 6y)(x + 5y)
c.
(x - 11y) (x + 30y)
d.
(5x - 6y) (4x - 5y)


Solution:

20x2 - 49xy + 30y2

= 20x2 - 25xy - 24xy + 30y2
[Express - 49xy as - 25xy - 24xy.]

= 5x(4x - 5y) - 6y(4x - 5y)
[Factor.]

= (5x - 6y) (4x - 5y)
[Factor again.]


Correct answer : (4)
 27.  
Factor:
- 3645v3 + 5000
a.
(81v - 10) (81v2 + 90v + 100)
b.
(9v + 10) (81v2 + 90v + 100)
c.
- 5 (9v - 10) (v2 - 90v)
d.
- 5(9v - 10) (81v2 + 90v + 100)


Solution:

- 3645v3 + 5000

= - 5(729v3 - 1000)
[GCF is - 5.]

= - 5 [(9v)3 - (10)3]
[Write as perfect cubes.]

= - 5 (9v - 10) (81v2 + 90v + 100)
[ a3 - b3 = (a - b) (a2 + ab + b2)]


Correct answer : (4)
 28.  
Factor:
x2 + 2xy - 15y2
a.
(x - y) (x + 15y)
b.
(x - 5y) (x + 3y)
c.
(x - 3y) (x - 15y)
d.
(x - 3y) (x + 5y)


Solution:

x2 + 2xy - 15y2

= x2 + 5xy - 3xy - 15y2
[Express 2xy as 5xy - 3xy.]

= x(x + 5y) - 3y (x + 5y)
[Factor.]

= (x - 3y) (x + 5y)
[Factor again.]


Correct answer : (4)
 29.  
Factor:
- 10x5 + 270x2
a.
- 3x (x2 - 3) (x2 + 3x + 9)
b.
- (x3 - 30) (10x2 + 3x + 9)
c.
(x - 5) (x2+ 5x + 25)
d.
- 10x2 (x - 3) (x2 + 3x + 9)


Solution:

- 10x5 + 270x2

= - 10x2 (x3 - 27)
[GCF is - 10x2.]

= - 10x2 (x - 3) (x2 + 3x + 9)
[a3 - b3 = (a - b) (a2 + ab + b2).]


Correct answer : (4)
 30.  
Factor:
- 7z3 + 21z2v + 70zv2
a.
- 7z (z + 2v) (z - 5v)
b.
- 7z (z + 2v) (z - 2v)
c.
- 2z (z - 2v) (z - 2v)
d.
7z (z + 10v) (z - 5v)


Solution:

- 7z3 + 21z2v + 70zv2

= - 7z (z2 - 3zv - 10v2)
[GCF is - 7 z.]

= - 7z (z2 - 5zv + 2zv - 10v2)
[Express - 3zv as - 5zv + 2zv.]

= - 7z [z(z - 5v) + 2v (z - 5v)]
[Factor.]

= - 7z (z + 2v) (z - 5v)
[Factor again.]


Correct answer : (1)

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