﻿ Factoring Polynomials Word Problems - Page 2 | Problems & Solutions

# Factoring Polynomials Word Problems - Page 2

Factoring Polynomials Word Problems
• Page 2
11.
Factor:

 a. (4$x$ -  $y$) (16$x$2 + $x$ + $y$ + $y$2) b. (64$x$3 +  $y$2)$y$3 c. (4$x$ -  $y$) (16$x$2 + 4$x$$y$ - 4$x$ -  $y$ +  $y$2) d. (4$x$ -  $y$) (16$x$2 +  $y$2)

#### 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.]

12.
Factor:
25$x$2 + 40$x$$y$ - 81$z$2 + 16$y$2
 a. (5$x$ + 4$y$) (5$x$ + 4$y$ + 9$z$) b. (5$x$ + 4$y$ - 9$z$) (5$x$ + 4$y$ + 9$z$) c. (5$x$ + 4$y$ - 9$z$) (5$x$ + 4$y$) d. (25$x$2 - 4$x$$y$ ) (5$z$2 + 16$y$2)

#### 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)]

13.
Factor:
- $x$2 - 15$x$ + 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)

14.
Factor:
- 16$x$4 + 105$x$2 - 125
 a. (5 - $x$2) (4$x$ - 5) (4$x$ + 5) b. ($x$ - 5)($x$ + 5) (5$x$ - 4) (5$x$ + 4) c. (5$x$2 - 4) (5$x$2 + 4) d. (5 - $x$2) ($x$ - 5) (5$x$ - 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)]

15.
Factor:
36$w$2 - 24$w$ - 16$z$2 + 4
 a. (6$w$ + 4$z$ - 2) (6$w$ - 4$z$ - 2) b. (36$w$2 - 24$w$)(16$z$2 + 2) c. (6$w$ + 2) (6$w$ - 4$z$ - 2) d. (36$w$ + 4$z$ - 2) ($w$ - 4$z$)

#### 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)

16.
Factor completely.
343$q$2 $l$2 - 63$q$2
 a. (7$l$ + 3) (49$q$2 $l$ - 21) b. 49$q$2 (7$l$ + 3) c. 7$q$2 (7$l$ + 3) (7$l$ - 3) d. (7$q$$l$ + 3) (49$q$$l$ - 21$q$2)

#### Solution:

343q2 l2 - 63q2

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

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

17.
Factor completely.
343$p$$m$2 - 784$p$$m$ + 448$p$
 a. 7$m$($p$ - 7)2 b. 7$p$(7$m$ - 8)2 c. $p$(7$m$ - 7)2 d. 7$m$(7$m$ - 8)(7$m$ + 8)

#### Solution:

343pm2 - 784pm + 448p

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

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

18.
Factor:
6$b$2 + 12$b$ - 48
 a. 6($b$ + 8)($b$ - 4) b. (6$b$ + 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)

19.
Factor completely.
44$x$4 - 1529$x$2 - 1980
 a. 11$x$ (4$x$2 + 144$x$ + 36) b. 11(4$x$2 + 5) ($x$2 - 144) c. 11($x$2 + 5) (4$x$ + 6) ($x$ - 6) d. 11(4$x$2 + 5) ($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)]

20.
Factor:
17$k$3 - 3$m$3 + 3$k$2 $m$ - 17$k$$m$2
 a. (17$k$ + 3$m$) ($k$ + $m$) ($k$ - $m$) b. (17$k$ + 3$m$) ($k$2 + 17$m$) c. (17$k$ + $m$) ($k$ + 3$m$) ($k$ - $m$) d. (17$k$ - 3$m$) ($k$ - $m$)

#### 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)]