Factoring Polynomials Worksheet

Factoring Polynomials Worksheet
• Page 1
1.
Factor: $x$3 - 343
 a. $x$3 - 21$x$2 + 147$x$ - 343 b. $x$3 + 21$x$2 + 147$x$ + 343 c. ($x$ - 7)($x$2 + 7$x$ + 49) d. ($x$ - 7)($x$2 - 7$x$ + 49)

Solution:

x3 - 343

= x3 - 73
[Write the terms as the difference between cubes.]

= (x - 7)(x2 + 7x + 49)
[Using (a3 - b3) = (a - b) (a2 + ab + b2).]

2.
Find the value of $a$ that makes $a$$x$2 - 20$x$ + 25 a perfect square.
 a. 4 b. 2 c. 20 d. 1

3.
Find the value of $b$ that makes $x$2 + $b$$x$ + 36 a perfect square.
 a. 12 b. 24 c. 6 d. 16

4.
Express as a perfect square.
$y$2 + 18$y$ + 81
 a. b. $y$($y$ + 9) c. d.

5.
Express as a perfect square.
$\frac{{z}^{2}}{{q}^{2}}$ + $\frac{5z}{q}$ + 6.25
 a. b. c. d.

6.
Express as a perfect square.
 a. b. c. d.

7.
Express as a perfect square.

 a. b. c. d.

8.
Express as a perfect square.
${k}^{2}-\frac{16k}{7}+\frac{64}{49}$
 a. b. c. d.

9.
Factor 8$d$$n$ + 7 + 9$d$$n$ +2, assume all exponents are positive integers.
 a. $d$$n$ - 9[8$d$5+ 9] b. $d$$n$ + 2[8$d$5 + 9] c. $d$$n$ + 9[8$d$5 + 9] d. $d$$n$ - 2[8$d$5 + 9]

Factor 3$d$$n$ +10 + 6$d$$n$ +5, assume all exponents are positive integers.
 a. $d$$n$ + 5[2$d$5+ 5] b. $d$$n$ - 5[2$d$5 +6] c. $d$$n$ - 5[2$d$5 + 5] d. 3$d$$n$ + 5[$d$5 + 2]