﻿ Factoring Polynomials Word Problems - Page 3 | Problems & Solutions

# Factoring Polynomials Word Problems - Page 3

Factoring Polynomials Word Problems
• Page 3
21.
Factor:
$c$5 - 36$c$3 + 8$c$2 - 288
 a. ($c$ + 2) ($c$2 - 2$c$ + 4) ($c$2 - 6) b. ($c$ + 2) ($c$2 - 2$c$ + 4) ($c$ - 6) ($c$ + 6) c. ($c$ + 2) ($c$2 - 2$c$ + 2) ($c$ - 2) ($c$ + 2) d. ($c$ - 2) ($c$2 + 2$c$ + 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)]

22.
Factor:
0.3$x$2 - 3.6$x$ + 9.6
 a. 1.2($x$ - 4)($x$ - 4) b. (0.3$x$ - 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)

23.
Factor:
9$a$$x$3 - 243$a$ + 10$b$$x$3 - 270$b$
 a. (9$a$$x$ + 10$b$) ($x$ - 3) ($x$ + 3) b. (9$a$ + 10$b$) ($x$ - 3) ($x$2 + 3$x$ + 9) c. ($a$ + $b$) ($x$ - 3) ($x$2 + 3) d. $\mathrm{ab}$($x$3 - 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)]

24.
Factor:
$b$4 - 625
 a. ($b$2 + 4) ($x$ - 25) ($x$ + 25) b. ($b$2 + 5) ($b$ - 5) ($b$ + 5) c. ($b$2 + 25) ($b$ - 5) ($b$ + 5) d. ($b$2 + 625) ($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)]

25.
Factor:
$b$16 - 16
 a. ($b$8 + 4) ($b$4 - 2) ($b$4 + 2) b. ($b$8 - 2) ($b$8 + 8) c. ($b$8 + 4) ($b$8 - 2) d. ($b$8 + 2) ($b$4 - 4) ($b$4 + 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).]

26.
Factor:
20$x$2 - 49$\mathrm{xy}$ + 30$y$2
 a. ($x$ - 5)2 b. ($x$ - 6$y$)($x$ + 5$y$) c. ($x$ - 11$y$) ($x$ + 30$y$) d. (5$x$ - 6$y$) (4$x$ - 5$y$)

#### 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.]

27.
Factor:
- 3645$v$3 + 5000
 a. (81$v$ - 10) (81$v$2 + 90$v$ + 100) b. (9$v$ + 10) (81$v$2 + 90$v$ + 100) c. - 5 (9$v$ - 10) ($v$2 - 90$v$) d. - 5(9$v$ - 10) (81$v$2 + 90$v$ + 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)]

28.
Factor:
$x$2 + 2$x$$y$ - 15$y$2
 a. ($x$ - $y$) ($x$ + 15$y$) b. ($x$ - 5$y$) ($x$ + 3$y$) c. ($x$ - 3$y$) ($x$ - 15$y$) d. ($x$ - 3$y$) ($x$ + 5$y$)

#### 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.]

29.
Factor:
- 10$x$5 + 270$x$2
 a. - 3$x$ ($x$2 - 3) ($x$2 + 3$x$ + 9) b. - ($x$3 - 30) (10$x$2 + 3$x$ + 9) c. ($x$ - 5) ($x$2+ 5$x$ + 25) d. - 10$x$2 ($x$ - 3) ($x$2 + 3$x$ + 9)

#### Solution:

- 10x5 + 270x2

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

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

30.
Factor:
- 7$z$3 + 21$z$2$v$ + 70$z$$v$2
 a. - 7$z$ ($z$ + 2$v$) ($z$ - 5$v$) b. - 7$z$ ($z$ + 2$v$) ($z$ - 2$v$) c. - 2$z$ ($z$ - 2$v$) ($z$ - 2$v$) d. 7$z$ ($z$ + 10$v$) ($z$ - 5$v$)

#### 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.]