﻿ Factoring Worksheets - Page 2 | Problems & Solutions

# Factoring Worksheets - Page 2

Factoring Worksheets
• Page 2
11.
Factor:
16$z$2 - 225$y$2
 a. (16$z$ - $y$)($z$ - 9$y$) b. (4$z$ + 15$y$)(4$z$ - 15$y$) c. (4$z$ - 3$y$)2 d. (4$z$ + 3$y$)2

12.
Express as a perfect square:
 a. b. c. d.

13.
Express the following as a perfect square.

 a. b. c. d.

14.
Express the following as a perfect square.
$\frac{y²}{z²}$ + $\frac{5.8y}{z}$ + 8.41
 a. b. c. d.

15.
Two square playgrounds have areas of 4$x$2 and 9$y$2. Express the difference in area in a factored form.
 a. 5$x$2$y$2 b. (2$x$ - 3$y$)(2$x$ + 3$y$) c. (4$x$ - 9$y$)2 d. (2$x$ - 3$y$)2

16.
Factor the expression 4${n}^{5}$ + 8${n}^{4}$ - 2${n}^{2}$ - 6$n$ - 4 completely.
 a. 2(2${n}^{4}$ + $n$ + 1)($n$ + 2) b. 2(${n}^{3}$ + 2${n}^{2}$ + 2$n$ + 1)($n$ - 2)($n$ + 1) c. 2(2${n}^{4}$ - $n$ + 1)($n$ + 2) d. 2(2${n}^{3}$ + 2${n}^{2}$ + 2$n$ + 1)($n$ + 2)($n$ - 1)

17.
Factor.
6${a}^{5}$ + 12${a}^{3}$ - 3${a}^{2}$
 a. 3${a}^{2}$(2${a}^{3}$ + 4$a$ + 1) b. 3${a}^{2}$(2${a}^{3}$ - 4$a$ + 1) c. 3${a}^{2}$(2${a}^{3}$ + 4$a$ - 1) d. 3${a}^{2}$(2${a}^{3}$ - 4$a$ - 1)

18.
Factor the expression completely.
- 4${w}^{4}$ + 28${w}^{3}$
 a. - 4${w}^{3}$($w$ - 7) b. - 4${w}^{3}$($w$ + 7) c. - 4${w}^{3}$($w$ - 1) d. 4${w}^{3}$($w$ - 7)

19.
Factor.
9${x}^{4}$ + 18$x$
 a. 3(3${x}^{4}$ + 6) b. 9$x$(${x}^{3}$ + 2) c. 9$x$(${x}^{3}$ - 2) d. 3${x}^{2}$(3${x}^{2}$ + 6)

Factor 289$a$2 + 238$a$$b$ + 119$c$$a$ + 49$c$$b$ + 49$b$2 completely.
 a. (17$a$ + 7$c$) (17$a$ - 7$b$ - 7$c$) b. (17$a$ + 7$b$) (17$a$ + 7$b$ + 7$c$) c. (17$a$ + 7$b$ + 7$c$)(7$c$ + 7$b$) d. (17$a$ - 7$b$) (17$a$ + 7$b$ + 7$c$)