Deck 5: Polynomials: Factoring

Question 1

Find the GCF.

- $7 x^{4},-14 x^{3}$

A) $7 \mathrm{x}^{3}$
B) $7 \mathrm{x}^{4}$
C) $5 x^{3}$
D) $-14 x^{4}$

Answer 1

$7 \mathrm{x}^{3}$

Question 2

Find the GCF.

- $-x^{2},-2 x,-16 x^{4}$

A) $-2 \mathrm{x}$
B) $-\mathrm{x}$
C) $-x^{2}$
D) $-2 x^{2}$

Answer 2

$-\mathrm{x}$

Question 3

Find the GCF.

- $x^{7} y^{7}, x^{6} y^{5}, x^{6} y^{6},-x^{2} y^{2}$

A) $x^{2} y^{2}$
B) $x^{6} y^{5}$
C) $-\mathrm{xy}$
D) $x^{5} y^{5}$

Answer 3

$x^{2} y^{2}$

Question 4

Factor.

- $3 y-12$

A) 3y
B) 12
C) No common factor
D) $3(y-4)$

Question 5

Factor.

- $5 x^{2}+25 x$

A) $5 x^{2}(x+5)$
B) $x(5 x+25)$
C) $5 x(x+25)$
D) $5 x(x+5)$

Question 6

Factor.

- $12 m^{9}-24 m^{7}+18 m^{5}$

A) No common factor
B) $6 m^{5}\left(2 m^{4}-4 m^{2}+3\right)$
C) $m^{5}\left(12 m^{4}-24 m^{2}+18\right)$
D) $6\left(2 m^{9}-4 m^{7}+3 m^{5}\right)$

Question 7

Factor.

- $36 m^{7}+42 m^{4}+12 m^{2}$

A) $6 m^{2}\left(6 m^{5}+7 m^{2}+2\right)$
B) No common factor
C) $6\left(6 m^{7}+7 m^{4}+2 m^{2}\right)$
D) $m^{2}\left(36 m^{5}+42 m^{2}+12\right)$

Question 8

Factor.

- $21 m^{2}-17 r^{3}$

A) $2\left(10 m^{2}+8 r^{3}\right)$
B) $\mathrm{m}^{2}(21-17 \mathrm{~m})$
C) No common factor
D) $3\left(7 m^{2}-5 r^{3}\right)$

Question 9

Factor.

- $3 x^{2} y^{6}+21 x^{2} y^{5}$

A) $3 x^{5} y^{2}(y+7)$
B) $3 x^{2} y^{5}(y+7)$
C) $y+7$
D) $x^{2} y^{5}(3 y+7)$

Question 10

Factor.

- $72 x^{9} y 9-24 x^{6} y^{4}-84 x^{2} y^{2}$

A) $12\left(6 x^{9} y^{9}-2 x^{6} y^{4}-7 x^{2} y^{2}\right)$
B) No common factor
C) $12 x^{2}\left(6 x^{7} y^{9}-2 x^{4} y^{4}-7 y^{2}\right)$
D) $12 x^{2} y^{2}\left(6 x^{7} y^{7}-2 x^{4} y^{2}-7\right)$

Question 11

Factor.

- $b^{8}-31 bm^{6}+29 b^{3} m^{8}-37 b^{8} m^{6}$

A) $b m\left(b^{7}-31 m^{5}+29 b^{2} m^{7}-37 b^{7} m^{5}\right)$
B) $b m^{6}\left(b^{7}-31+29 b^{2} m^{2}-37 b^{7}\right)$
C) $b^{2}\left(b^{7}-31 m^{5}+29 b^{2} m^{7}-37 b^{7} m^{5}\right)$
D) $b\left(b^{7}-31 m^{6}+29 b^{2} m^{8}-37 b^{7} m^{6}\right)$

Question 12

Factor.

- $\frac{5}{3} \mathrm{x}^{11}-\frac{4}{3} \mathrm{x}^{10}+\frac{5}{3} \mathrm{x}^{9}+\frac{1}{3} \mathrm{x}^{8}$

A) $\frac{1}{3} x^{9}\left(5 x^{3}+4 x^{2}-5 x-1\right)$
B) $\frac{1}{3} x^{8}\left(5 x^{3}-4 x^{2}+5 x+1\right)$
C) $\frac{5}{3} x^{8}\left(x^{3}-3 x^{2}+4 x+1\right)$
D) $\frac{1}{3} x^{9}\left(5 x^{4}-4 x^{3}+5 x^{2}+x\right)$

Question 13

Factor.

- $3 x(6 x+5)-2(6 x+5)$

A) $(3 x+2)(6 x-5)$
B) $(18 x+2)(x-5)$
C) $(18 x-2)(x+5)$
D) $(3 x-2)(6 x+5)$

Question 14

Factor.

- $\mathrm{t}(3-\mathrm{m})+\mathrm{s}(3-\mathrm{m})$

A) No common factor
B) $\mathrm{t}(3-\mathrm{m})+\mathrm{s}$
C) $(\mathrm{t}+\mathrm{s})(3-\mathrm{m})$
D) $(\mathrm{t}-\mathrm{s})(3-\mathrm{m})$

Question 15

Factor.

- $2 m(7-m)+3 n(7-m)$

A) $m(2+3 n)(7-1)$
B) $(2 m-3 n)(7-m)$
C) No common factor
D) $(2 m+3 n)(7-m)$

Question 16

Factor by grouping.

- $x^{3}+8 x^{2}+7 x+56$

A) $(x+8 x)\left(x^{2}+7\right)$
B) $(\mathrm{x}-8)\left(\mathrm{x}^{3}+7\right)$
C) $(x+8)\left(x^{2}+7\right)$
D) $(x+8)\left(x^{2}-7\right)$

Question 17

Factor by grouping.

- $x^{3}+2 x^{2}-6 x-12$

A) $\left(x^{2}+2\right)(x-6)$
B) $(x-2)\left(x^{2}-6\right)$
C) $(x+2)\left(x^{3}-6 x\right)$
D) $(x+2)\left(x^{2}-6\right)$

Question 18

Factor by grouping.

- $x^{3}-7 x^{2}-10 x+70$

A) $(x-7)\left(x^{2}+10 x\right)$
B) $(x-7)\left(x^{2}-10\right)$
C) $(x+7)\left(x^{3}-10\right)$
D) $(x+7)\left(x^{2}+10\right)$

Question 19

Factor by grouping.

- $x^{3}-3 x^{2}+4 x-12$

A) $(x-12)\left(x^{2}-3 x+4\right)$
B) $(x-3)\left(x^{2}+4\right)$
C) $(x-3)\left(x^{2}+3\right)$
D) $(x+3)\left(x^{2}+4\right)$

Question 20

Factor by grouping.

- $2 x^{3}-18 x^{2}-5 x+45$

A) Not possible
B) $(x+45)\left(x^{2}-18 x-5\right)$
C) $(x-9)\left(2 x^{2}-5\right)$
D) $(x+9)\left(2 x^{2}-5\right)$

Question 21

Factor.

- $x^{2}-x-42$

A) $(x+6)(x-7)$
B) $(x+1)(x-42)$
C) Prime
D) $(x+7)(x-6)$

Question 22

Factor.

- $x^{2}+8 x-48$

A) $(x+12)(x-4)$
B) $(x-12)(x+1)$
C) Prime
D) $(x-12)(x+4)$

Question 23

Factor.

- $x^{2}-8 x-33$

A) $(x+3)(x-11)$
B) $(x-3)(x+1)$
C) $(x-3)(x+11)$
D) Prime

Question 24

Factor.

- $x^{2}-x-54$

A) $(x-6)(x+9)$
B) Prime
C) $(x-54)(x+1)$
D) $(x+6)(x-9)$

Question 25

Factor.

- $7 x^{2}-7 x-42$

A) $7(x-2)(x+3)$
B) $(7 x+14)(x-3)$
C) $7(x+2)(x-3)$
D) Prime

Question 26

Factor.

- $3 x^{2}-15 x+18$

A) $3(x-6)(x+1)$
B) Prime
C) $(3 x-6)(x-3)$
D) $3(x-2)(x-3)$

Question 27

Factor.

- $24-5 x-x^{2}$

A) $(x+8)(x-3)$
B) $(-x-8)(x-3)$
C) $(x-8)(x-3)$
D) $(-x-3)(x-8)$

Question 28

Factor.

- $4 x^{3}+4 x^{2}-24 x$

A) $4 x(x-2)(x+3)$
B) $4 x(x+2)(x-3)$
C) Prime
D) $\left(4 x^{2}+8 x\right)(x-3)$

Question 29

Factor.

- $x^{3}-x^{2}-30 x$

A) Prime
B) $x(x+5)(x-6)$
C) $\left(x^{2}+1\right)(x-30)$
D) $x(x+6)(x-5)$

Question 30

Factor.

- $x^{3}+5 x^{2}-84 x$

A) $\left(x^{2}+12\right)(x-7)$
B) $\left(x^{2}+7\right)(x-12)$
C) $x(x+12)(x-7)$
D) $x(x-12)(x+7)$

Question 31

Factor.

- $\mathrm{p}^{4}-15 \mathrm{p}^{2}+56$

A) $\left(p^{2}-7\right)\left(p^{2}+8\right)$
B) $\left(p^{2}-7\right)\left(p^{2}-8\right)$
C) $\left(p^{2}-56\right)\left(p^{2}-1\right)$
D) $p^{2}(p-7)(p-8)$

Question 32

Factor.

- $4 x^{6}-40 x^{5}-96 x^{4}$

A) $4 x^{4}(x-6)(x-4)$
B) $4 x^{4}\left(x^{2}-4 x-24\right)$
C) $4 x^{4}(x-6)(x+4)$
D) $4 x^{3}\left(x^{2}-4 x-24\right)$

Question 33

Factor.

- $x^{2}+2 x y-15 y^{2}$

A) $(x-y)(x+3 y)$
B) $(x+5 y)(x-3 y)$
C) $(x-5 y)(x+y)$
D) $(x-5 y)(x+3 y)$

Question 34

Factor.

- $u^{2}-5 u v-24 v^{2}$

A) $(u-v)(u+8 v)$
B) $(u-3 v)(u+v)$
C) $(u+3 v)(u-8 v)$
D) $(u-3 v)(u+8 v)$

Question 35

Factor.

- $u^{2}-3 u v-54 v^{2}$

A) $(u+6 v)(u-9 v)$
B) $(u-v)(u+9 v)$
C) $(u-6 v)(u+9 v)$
D) $(u-6 v)(u+v)$

Question 36

Factor.

- $x^{2}+3 x y-130 y^{2}$

A) $(x-13 y)(x+y)$
B) $(x-13 y)(x+10 y)$
C) $(x+13 y)(x-10 y)$
D) $(x-y)(x+10 y)$

Question 37

Factor.

- $x^{2}+3 x y-18 y^{2}$

A) $(x-6 y)(x+3 y)$
B) $(x-y)(x+3 y)$
C) $(x-6 y)(x+y)$
D) $(x+6 y)(x-3 y)$

Question 38

Factor.

- $u^{2}-4 u v-12 v^{2}$

A) $(u-2 v)(u+6 v)$
B) $(u-v)(u+6 v)$
C) $(u+2 v)(u-6 v)$
D) $(u-2 v)(u+v)$

Question 39

Factor.

- $x^{2}-4 x y-21 y^{2}$

A) $(x-7 y)(x+3 y)$
B) $(x-y)(x+3 y)$
C) $(x+7 y)(x-3 y)$
D) $(x-7 y)(x+y)$

Question 40

Factor.

- $x^{2}+\frac{2}{11} x+\frac{1}{121}$

A) Prime
B) $x\left(x+\frac{2}{11}\right)$
C) $\left(x+\frac{1}{11}\right)^{2}$
D) $\left(x+\frac{2}{11}\right)^{2}$

Question 41

Factor.

- $y^{2}-\frac{2}{7} y+\frac{1}{49}$

A) y $\left(y-\frac{2}{7}\right)$
B) Prime
C) $\left(y+\frac{1}{7}\right)^{2}$
D) $\left(y-\frac{1}{7}\right)^{2}$

Question 42

Factor.

- $x^{2}+\frac{6}{7} x+\frac{9}{49}$

A) $\left(x^{2}+\frac{3}{7}\right)^{2}$
B) $\left(x+\frac{3}{7}\right)\left(x+\frac{3}{7} x\right)$
C) $\left(x+\frac{6}{7}\right)\left(x+\frac{3}{7}\right)$
D) $\left(x+\frac{3}{7}\right)^{2}$

Question 43

Factor.

- $x^{2}+\frac{6}{7} x+\frac{9}{49}$

A) $\left(x+\frac{6}{7}\right)\left(x+\frac{3}{7}\right)$
B) $\left(x+\frac{3}{7}\right)\left(x+\frac{3}{7} x\right)$
C) $\left(x^{2}+\frac{3}{7}\right)^{2}$
D) $\left(x+\frac{3}{7}\right)^{2}$

Question 44

Factor.

- $t^{2}+1.4 t+0.49$

A) $\left(t^{2}+0.7\right)^{2}$
B) $(t+0.7)^{2}$
C) $(t+1.4)^{2}$
D) $t(t+1.4)$

Question 45

Factor.

- $y^{2}+1.4 y+0.49$

A) $(y+1.4)^{2}$
B) $y(y+1.4)$
C) $(y+0.7)^{2}$
D) $\left(y^{2}+0.7\right)^{2}$

Question 46

Factor.

- $t^{2}+1.1 t+0.3$

A) Prime
B) $(t+1.1)(t+0.3)$
C) $(t+0.6)(t+0.5)$
D) $(t+0.55)^{2}$

Question 47

Factor.

- $y^{2}+0.3 y-0.4$

A) $(y-0.8)(y+0.5)$
B) $(y+0.8)(y-0.5)$
C) $(\mathrm{y}-0.8)(\mathrm{y}-0.5)$
D) $(y+0.15)^{2}$

Question 48

Factor.

- $t^{2}+0.4 t-0.12$

A) $(t-0.6)(t+0.2)$
B) $(t+0.6)(t-0.2)$
C) $(t+0.12)(t-1)$
D) $(t+0.2)^{2}$

Question 49

Factor.

- $x^{2}-0.9 x+0.2$

A) $(x-0.4)(x+0.5)$
B) $(x-0.4)(x-0.5)$
C) $(x+0.4)(x-0.5)$
D) $(x-0.45)^{2}$

Question 50

Factor.

- $15 x^{2}+22 x+8$

A) Prime
B) $(3 x+2)(5 x+4)$
C) $(3 \mathrm{x}-2)(5 \mathrm{x}-4)$
D) $(15 x+2)(x+4)$

Question 51

Factor.

- $12 y^{2}+17 y+6$

A) $(4 y-3)(3 y-2)$
B) $(12 y+3)(y+2)$
C) Prime
D) $(4 y+3)(3 y+2)$

Question 52

Factor.

- $10 \mathrm{z}^{2}+7 \mathrm{z}-12$

A) Prime
B) $(2 z+3)(5 z-4)$
C) $(10 z+3)(z-4)$
D) $(2 z-3)(5 z+4)$

Question 53

Factor.

- $20 z^{2}-3 z-9$

A) $(4 z+3)(5 z-3)$
B) Prime
C) $(4 z-3)(5 z+3)$
D) $(20 z-3)(z+3)$

Question 54

Factor.

- $9 x^{2}-9 x-54$

A) $(x+2)(9 x-27)$
B) $9(x+2)(x-3)$
C) $(9 x+18)(x-3)$
D) $9(x-2)(x+3)$

Question 55

Factor.

- $6 x^{2}-26 x-20$

A) $2(3 x+2)(x-5)$
B) $2(3 x-2)(x+5)$
C) $(3 x+2)(2 x-10)$
D) $(6 x+4)(x-5)$

Question 56

Factor.

- $10 x^{2}-35 x-20$

A) $5(2 x-1)(x+4)$
B) $(2 x-1)(5 x+20)$
C) $(10 x-5)(x+4)$
D) $5(2 x+1)(x-4)$

Question 57

Factor.

- $18 y^{2}+81 y-45$

A) $9(2 y+1)(y-5)$
B) $(2 y-1)(9 y+45)$
C) $9(2 y-1)(y+5)$
D) $(18 y-9)(y+5)$

Question 58

Factor.

- $-36 x^{2}-30 x+36$

A) $6(3 x+2)(-2 x+3)$
B) $6(-3 x+2)(2 x+3)$
C) $(-3 x+2)(12 x+18)$
D) $(-18 \mathrm{x}+12)(2 \mathrm{x}+3)$

Question 59

Factor.

- $4 x^{2}-7 x+8$

A) Prime
B) $(2 x-8)(2 x-1)$
C) $(4 \mathrm{x}-1)(\mathrm{x}-8)$
D) $(4 x-8)(x-1)$

Question 60

Factor.

- $16-72 x+81 x^{2}$

A) $(9 x-4)^{2}$
B) Prime
C) $(81 \mathrm{x}-4)(\mathrm{x}-4)$
D) $(9 \mathrm{x}+4)^{2}$

Question 61

Factor.

- $25 z^{4}-5 z^{2}-12$

A) $\left(5 z^{4}+3\right)(5 z-4)$
B) $\left(5 z^{2}+3\right)\left(5 z^{2}-4\right)$
C) $\left(5 z^{4}+4\right)(5 z-3)$
D) $\left(5 z^{2}+4\right)\left(5 z^{2}-3\right)$

Question 62

Factor.

- $8 x^{3}+18 x^{2}+9 x$

A) $x(4 x+3)(2 x+3)$
B) $x(8 x+1)(x+9)$
C) $x(4 x-3)(2 x-3)$
D) $\left(8 x^{2}+3\right)(x+3)$

Question 63

Factor.

- $12 z^{3}+7 z^{2}-12 z$

A) $z(12 z+1)(z-12)$
B) $\left(z^{2}-3\right)(12 z+4)$
C) $(3 z-4)(4 z+3)$
D) $z(3 z+4)(4 z-3)$

Question 64

Factor.

- $9 x^{4}-18 x^{3}+8 x^{2}$

A) $\left(9 x^{2}+2\right)\left(x^{2}+4\right)$
B) $x^{2}(9 x-1)(x-8)$
C) $x^{2}(3 x-2)(3 x-4)$
D) $x(3 x+2)(3 x+4)$

Question 65

Factor.

- $5 x^{3}+15 x^{2}-50 x$

A) $5 x(x-2)(x+5)$
B) $\left(5 x^{2}+10 x\right)(x-5)$
C) $5 x(x+2)(x-5)$
D) $(x-2)\left(5 x^{2}+25\right)$

Question 66

Factor.

- $2 a^{3}+6 a^{2}-8 a$

A) $2 a(a-4)(a-1)$
B) $2 a(a-4)(a+1)$
C) $2 a(a+4)(a-1)$
D) $2 \mathrm{a}(\mathrm{a}+4)(\mathrm{a}+1)$

Question 67

Factor.

- $18 x^{3}-78 x^{2}-60 x$

A) $\left(x^{2}-5\right)(18 x+12)$
B) $x(3 x+2)(6 x-30)$
C) $6(3 x-2)(x+5)$
D) $6 x(3 x+2)(x-5)$

Question 68

Factor.

- $3 x^{4}-18 x^{3}+24 x^{2}$

A) $3 x^{2}(x-4)(x-2)$
B) $3 x^{2}(x-4)(x+2)$
C) $3 x^{2}(x+4)(x+2)$
D) $3 x^{2}(x+4)(x-2)$

Question 69

Factor.

- $24 z^{6}+52 z^{4}+24 z^{2}$

A) $4 z^{2}\left(2 z^{2}-3\right)\left(3 z^{2}-2\right)$
B) $4\left(3 z^{4}+2\right)\left(2 z^{2}+3\right)$
C) $\left(12 z^{3}+8\right)\left(2 z^{3}+3\right)$
D) $4 z^{2}\left(3 z^{2}+2\right)\left(2 z^{2}+3\right)$

Question 70

Factor.

- $36 z^{8}+51 z^{5}+18 z^{2}$

A) $3 z^{2}\left(4 z^{3}+3\right)\left(3 z^{3}+2\right)$
B) $3\left(4 z^{6}+3\right)\left(3 z^{2}+2\right)$
C) $\left(4 z^{4}+4\right)\left(3 z^{4}+2\right)$
D) $3 z^{2}\left(3 z^{3}-2\right)\left(4 z^{3}-3\right)$

Question 71

Factor.

- $4 x^{2}-12 x y-16 y^{2}$

A) $(x-y)(4 x+12 y)$
B) $4(\mathrm{x}-\mathrm{y})(\mathrm{x}+4 \mathrm{y})$
C) $(4 x-4 y)(x+4 y)$
D) $4(x+y)(x-4 y)$

Question 72

Factor.

- $3 x^{2}-9 x y-12 y^{2}$

A) $(x-y)(3 x+9 y)$
B) $3(x+y)(x-4 y)$
C) $(3 x-3 y)(x+4 y)$
D) $3(x-y)(x+4 y)$

Question 73

Factor.

- $4 x^{2}-12 x t+9 t^{2}$

A) Prime
B) $(4 x-3 t)(x-3 t)$
C) $(2 x+3 t)(2 x+3 t)$
D) $(2 x-3 t)(2 x-3 t)$

Question 74

Factor.

- $6 x^{2}-5 x t-4 t^{2}$

A) $(6 x+t)(x-4 t)$
B) Prime
C) $(2 \mathrm{x}+\mathrm{t})(3 \mathrm{x}-4 \mathrm{t})$
D) $(2 \mathrm{x}-\mathrm{t})(3 \mathrm{x}+4 \mathrm{t})$

Question 75

Factor.

- $96 x^{2}+56 x y+8 y^{2}$

A) $(24 \mathrm{x}+8 \mathrm{y})(4 \mathrm{x}+\mathrm{y})$
B) $8(3 x-y)(4 x-y)$
C) $(3 x+y)(8 x+3 y)$
D) $8(3 x+y)(4 x+y)$

Question 76

Factor.

- $12 x^{2}+17 x y+6 y^{2}$

A) $(3 x-2 y)(4 x-3 y)$
B) $(12 x+2 y)(x+3 y)$
C) $(3 \mathrm{x}+2 \mathrm{y})(4 \mathrm{x}+3 \mathrm{y})$
D) $(12 x+y)(x+6 y)$

Question 77

Factor.

- $20 x^{2}-23 x y+6 y^{2}$

A) $(4 x+3 y)(5 x-2 y)$
B) $(4 x-3 y)(5 x-2 y)$
C) $(20 x+3 y)(x+2 y)$
D) $(4 x+3 y)(5 x+2 y)$

Question 78

Factor.

- $15 z^{2}-11 z y-12 y^{2}$

A) $(3 z+4 y)(5 z-3 y)$
B) $(15 z-4 y)(z+3 y)$
C) $(15 z+y)(z-12 y)$
D) $(3 z-4 y)(5 z+3 y)$

Question 79

Factor.

- $45 x^{2}+60 x y+20 y^{2}$

A) $5\left(9 x^{2}+12 x y+4 y\right)$
B) $5(3 x-2 y)(3 x+2 y)$
C) $5(3 x+2 y)^{2}$
D) $(15 x+10 y)(3 x+2 y)$

Question 80

Factor by grouping.

- $s^{2}+6 s+7 s+42$

A) $(s-6)(s-7)$
B) $(s+6)(s-7)$
C) $(s+6)(s+7)$
D) $\mathrm{s}(\mathrm{s}+55)$