Deck 11: Polynomials: Factoring

Question 1

Find the GCF.

- $2 x^{4}, 6 x^{2}$

A) $6 x^{4}$
B) $5 x^{2}$
C) $2 x^{4}$
D) $2 x^{2}$

Answer 1

$2 x^{2}$

Question 2

Find the GCF.

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

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

Answer 2

$-x$

Question 3

Find the GCF.

- $x^{5} y^{5}, x^{4} y^{3}, x^{4} y^{4},-x y$

A) $x^{4} y^{3}$
B) $-x y$
C) $x^{3} y^{3}$
D) $x y$

Answer 3

$x y$

Question 4

Factor.

- $2 y+8$

A) 8
B) No common factor
C) $2 y$
D) $2(y+4)$

Question 5

Factor.

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

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

Question 6

Factor.

- $12 m^{7}-6 m^{4}+14 m^{2}$

A) $2\left(6 m^{7}-3 m^{4}+7 m^{2}\right)$
B) No common factor
C) $m^{2}\left(12 m^{5}-6 m^{2}+14\right)$
D) $2 m^{2}\left(6 m^{5}-3 m^{2}+7\right)$

Question 7

Factor.

- $42 m^{9}+60 m^{6}+36 m^{3}$

A) $6 m^{3}\left(7 m^{6}+10 m^{3}+6\right)$
B) No common factor
C) $6\left(7 m^{9}+10 m^{6}+6 m^{3}\right)$
D) $m^{3}\left(42 m^{6}+60 m^{3}+36\right)$

Question 8

Factor.

- $22 m^{2}-15 r^{3}$

A) $3\left(7 m^{2}-5 r^{3}\right)$
B) $m^{2}(22-15 m)$
C) $2\left(11 \mathrm{~m}^{2}+7 \mathrm{r}^{3}\right)$
D) No common factor

Question 9

Factor.

- $3 x^{2} y^{7}+9 x^{2} y^{6}$

A) $3 x^{2} y^{6}(y+3)$
B) $3 x^{6} y^{2}(y+3)$
C) $y+3$
D) $x^{2} y^{6}(3 y+3)$

Question 10

Factor.

- $72 x^{7} y^{9}+60 x^{5} y^{5}+36 x^{2} y^{2}$

A) $12 x^{2} y^{2}\left(6 x^{5} y^{7}+5 x^{3} y^{3}+3\right)$
B) $12\left(6 x^{7} y^{9}+5 x^{5} y^{5}+3 x^{2} y^{2}\right)$
C) $12 x^{2}\left(6 x^{5} y^{9}+5 x^{3} y^{5}+3 y^{2}\right)$
D) No common factor

Question 11

Factor.

- $w^{7}-29 w a^{6}+7 w^{3} a^{7}-3 w^{7} a^{6}$

A) $w a^{6}\left(w^{6}-29+7 w^{2} a^{1}-3 w^{6}\right)$
B) $w a\left(w^{6}-29 a^{5}+7 w^{2} a^{6}-3 w^{6} a^{5}\right)$
C) $w^{2}\left(w^{6}-29 a^{5}+7 w^{2} a^{6}-3 w^{6} a^{5}\right)$
D) $w\left(w^{6}-29 a^{6}+7 w^{2} a^{7}-3 w^{6} a^{6}\right)$

Question 12

Factor.

- $\frac{5}{3} x^{12}-\frac{4}{3} x^{11}+\frac{5}{3} x^{10}+\frac{1}{3} x^{9}$

A) $\frac{5}{3} x^{9}\left(x^{3}-3 x^{2}+4 x+1\right)$
B) $\frac{1}{3} x^{9}\left(5 x^{3}-4 x^{2}+5 x+1\right)$
C) $\frac{1}{2} x^{10}\left(5 x^{3}+4 x^{2}-5 x-1\right)$
D) $\frac{1}{3} x^{10}\left(5 x^{4}-4 x^{3}+5 x^{2}+x\right)$

Question 13

Factor.

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

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

Question 14

Factor.

- $\mathfrak{t}(8-\mathrm{m})+\mathrm{s}(8-\mathrm{m})$

A) $\mathrm{t}(8-\mathrm{m})+\mathrm{s}$
B) No common factor
C) $(\mathrm{t}-\mathrm{s})(8-\mathrm{m})$
D) $(\mathrm{t}+\mathrm{s})(8-\mathrm{m})$

Question 15

Factor.

- $8 m(9-m)+9 n(9-m)$

A) $(8 m-9 n)(9-m)$
B) No common factor
C) $(8 m+9 n)(9-m)$
D) $m(8+9 n)(9-1)$

Question 16

Factor by grouping.

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

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

Question 17

Factor by grouping.

- $x^{3}+7 x^{2}-3 x-21$

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

Question 18

Factor by grouping.

- $x^{3}-2 x^{2}-5 x+10$

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

Question 19

Factor by grouping.

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

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

Question 20

Factor by grouping.

- $2 x^{3}-10 x^{2}-3 x+15$

A) $(x+15)\left(x^{2}-10 x-3\right)$
B) $(x-5)\left(2 x^{2}-3\right)$
C) Not possible
D) $(x+5)\left(2 x^{2}-3\right)$

Question 21

Factor.

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

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

Question 22

Factor.

- $x^{2}+4 x-60$

A) Prime
B) $(x-10)(x+1)$
C) $(x-10)(x+6)$
D) $(x+10)(x-6)$

Question 23

Factor.

- $x^{2}-4 x-45$

A) $(x-5)(x+9)$
B) Prime
C) $(x-5)(x+1)$
D) $(x+5)(x-9)$

Question 24

Factor.

- $4 x^{2}-28 x+48$

A) $(4 x-12)(x-4)$
B) $4(x-12)(x+1)$
C) $4(x-3)(x-4)$
D) Prime

Question 25

Factor.

- $7+6 x-x^{2}$

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

Question 26

Factor.

- $2 x^{3}+6 x^{2}-20 x$

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

Question 27

Factor.

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

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

Question 28

Factor.

- $x^{3}+8 x^{2}-33 x$

A) $\left(x^{2}+11\right)(x-3)$
B) $\left(x^{2}+3\right)(x-11)$
C) $x(x+11)(x-3)$
D) $x(x-11)(x+3)$

Question 29

Factor.

- $\mathrm{p}^{4}-11 \mathrm{p}^{2}+24$

A) $\left(p^{2}-3\right)\left(p^{2}-8\right)$
B) $p^{2}(p-3)(p-8)$
C) $\left(\mathrm{p}^{2}-3\right)\left(\mathrm{p}^{2}+8\right)$
D) $\left(p^{2}-24\right)\left(p^{2}-1\right)$

Question 30

Factor.

- $5 x^{9}-50 x^{8}-105 x^{7}$

A) $5 x^{7}\left(x^{2}-6 x-21\right)$
B) $5 x^{6}\left(x^{2}-6 x-21\right)$
C) $5 x^{7}(x-7)(x-3)$
D) $5 x^{7}(x-7)(x+3)$

Question 31

Factor.

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

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

Question 32

Factor.

- $u^{2}-3 u v-40 v^{2}$

A) $(u+5 v)(u-8 v)$
B) $(u-5 v)(u+v)$
C) $(u-v)(u+8 v)$
D) $(u-5 v)(u+8 v)$

Question 33

Factor.

- $u^{2}-5 u v-50 v^{2}$

A) $(u+5 v)(u-10 v)$
B) $(u-v)(u+10 v)$
C) $(u-5 v)(u+10 v)$
D) $(u-5 v)(u+v)$

Question 34

Factor.

- $x^{2}+4 x y-165 y^{2}$

A) $(x+15 y)(x-11 y)$
B) $(x-15 y)(x+y)$
C) $(x-15 y)(x+11 y)$
D) $(x-y)(x+11 y)$

Question 35

Factor.

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

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

Question 36

Factor.

- $y^{2}+0.4 y+0.04$

A) $\left(y^{2}+0.2\right)^{2}$
B) $(y+0.4)^{2}$
C) $y(y+0.4)$
D) $(y+0.2)^{2}$

Question 37

Factor.

- $t^{2}+1.2 t+0.35$

A) $(t+1.2)(t+0.35)$
B) $(t+0.5)(t+0.7)$
C) Prime
D) $(t+0.6)^{2}$

Question 38

Factor.

- $y^{2}+0.3 y-0.18$

A) $(y+0.15)^{2}$
B) $(y+0.6)(y-0.3)$
C) $(y-0.6)(y+0.3)$
D) $(y-0.6)(y-0.3)$

Question 39

Factor.

- $t^{2}+0.2 t-0.15$

A) $(t+0.15)(t-1)$
B) $(t+0.1)^{2}$
C) $(t-0.5)(t+0.3)$
D) $(t+0.5)(t-0.3)$

Question 40

Factor.

- $x^{2}-0.7 x+0.12$

A) $(x-0.4)(x+0.3)$
B) $(x+0.4)(x-0.3)$
C) $(x-0.4)(x-0.3)$
D) $(x-0.35)^{2}$

Question 41

Factor.

- $6 x^{2}+13 x+6$

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

Question 42

Factor.

- $12 y^{2}+25 y+12$

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

Question 43

Factor.

- $8 z^{2}-6 z-9$

A) $(4 z+3)(2 z-3)$
B) $(4 z-3)(2 z+3)$
C) Prime
D) $(8 z+3)(z-3)$

Question 44

Factor.

- $10 z^{2}-7 z-12$

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

Question 45

Factor.

- $6 x^{2}-6 x-36$

A) $(x+2)(6 x-18)$
B) $6(x+2)(x-3)$
C) $6(x-2)(x+3)$
D) $(6 x+12)(x-3)$

Question 46

Factor.

- $21 x^{2}-91 x-70$

A) $7(3 x+2)(x-5)$
B) $7(3 x-2)(x+5)$
C) $(3 x+2)(7 x-35)$
D) $(21 x+14)(x-5)$

Question 47

Factor.

- $18 x^{2}-63 x-36$

A) $(2 x-1)(9 x+36)$
B) $9(2 x-1)(x+4)$
C) $9(2 x+1)(x-4)$
D) $(18 x-9)(x+4)$

Question 48

Factor.

- $8 y^{2}+36 y-20$

A) $(2 y-1)(4 y+20)$
B) $(8 y-4)(y+5)$
C) $4(2 y+1)(y-5)$
D) $4(2 y-1)(y+5)$

Question 49

Factor.

- $-30 x^{2}-25 x+30$

A) $5(3 x+2)(-2 x+3)$
B) $(-15 x+10)(2 x+3)$
C) $5(-3 x+2)(2 x+3)$
D) $(-3 x+2)(10 x+15)$

Question 50

Factor.

- $4 x^{2}-5 x+9$

A) $(4 x-9)(x-1)$
B) $(4 x-1)(x-9)$
C) Prime
D) $(2 x-9)(2 x-1)$

Question 51

Factor.

- $81-126 x+49 x^{2}$

A) $(49 x-9)(x-9)$
B) $(7 x+9)^{2}$
C) Prime
D) $(7 x-9)^{2}$

Question 52

Factor.

- $8 z^{4}-6 z^{2}-9$

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

Question 53

Factor.

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

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

Question 54

Factor.

- $3 x^{3}+6 x^{2}-24 x$

A) $3 x(x-2)(x+4)$
B) $\left(3 x^{2}+6 x\right)(x-4)$
C) $3 x(x+2)(x-4)$
D) $(x-2)\left(3 x^{2}+12\right)$

Question 55

Factor.

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

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

Question 56

Factor.

- $3 x^{6}-33 x^{5}+90 x^{4}$

A) $3 x^{4}(x+6)(x-5)$
B) $3 x^{4}(x+6)(x+5)$
C) $3 x^{4}(x-6)(x+5)$
D) $3 x^{4}(x-6)(x-5)$

Question 57

Factor.

- $36 z^{6}+72 z^{4}+32 z^{2}$

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

Question 58

Factor.

- $60 z^{8}+93 z^{5}+36 z^{2}$

A) $3\left(4 z^{6}+3\right)\left(5 z^{2}+4\right)$
B) $3 z^{2}\left(5 z^{3}-4\right)\left(4 z^{3}-3\right)$
C) $\left(4 z^{4}+4\right)\left(5 z^{4}+4\right)$
D) $3 z^{2}\left(4 z^{3}+3\right)\left(5 z^{3}+4\right)$

Question 59

Factor.

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

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

Question 60

Factor.

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

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

Question 61

Factor.

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

A) $(4 x+3 y)(x+3 y)$
B) $(2 x+3 y)(2 x+3 y)$
C) $(2 x-3 y)(2 x-3 y)$
D) $(4 x+y)(x+9 y)$

Question 62

Factor.

- $6 x^{2}-13 x y+6 y^{2}$

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

Question 63

Factor.

- $9 z^{2}+6 z y-8 y^{2}$

A) $(3 z+2 y)(3 z-4 y)$
B) $(9 z+y)(z-8 y)$
C) $(9 z-2 y)(z+4 y)$
D) $(3 z-2 y)(3 z+4 y)$

Question 64

Factor.

- $36 x^{2}+48 x y+16 y^{2}$

A) $4\left(9 x^{2}+12 x y+4 y\right)$
B) $4(3 x+2 y)^{2}$
C) $4(3 x-2 y)(3 x+2 y)$
D) $(12 x+8 y)(3 x+2 y)$

Question 65

Factor by grouping.

- $t^{2}+8 t+4 t+32$

A) $(t+8)(t+4)$
B) $t(t+44)$
C) $(t-8)(t-4)$
D) $(t+8)(t-4)$

Question 66

Factor by grouping.

- $8 x^{2}+6 x-12 x-9$

A) $(8 x+3)(x-3)$
B) $(2 x+3)(4 x-3)$
C) $(8 x-3)(x+3)$
D) $(2 x-3)(4 x+3)$

Question 67

Factor by grouping.

- $6 x^{4}-4 x^{2}-15 x^{2}+10$

A) $\left(2 x^{4}-5\right)(3 x-2)$
B) $\left(2 x^{2}-5\right)\left(3 x^{2}-2\right)$
C) $\left(6 x^{2}+5\right)\left(x^{2}+2\right)$
D) $\left(2 x^{2}+5\right)\left(3 x^{2}+2\right)$

Question 68

Factor by grouping.

- $12 x^{2}+10 x y+18 x y+15 y^{2}$

A) $(2 x-3 y)(6 x+5 y)$
B) $(2 x+3 y)(6 x+5 y)$
C) $(2 x+3)(6 x+5)$
D) $(12 x+3 y)(x+5 y)$

Question 69

Factor using the ac-method.

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

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

Question 70

Factor using the ac-method.

- $9 z^{2}+6 z-8$

A) prime
B) $(3 z+4)(3 z-2)$
C) $(3 z-4)(3 z+2)$
D) $(9 z+4)(z-2)$

Question 71

Factor using the ac-method.

- $9 x^{2}-3 x t-2 t^{2}$

A) $(3 x-t)(3 x+2 t)$
B) $(3 x+t)(3 x-2 t)$
C) prime
D) $(9 x+t)(x-2 t)$

Question 72

Factor using the ac-method.

- $36-13 x+x^{2}$

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

Question 73

Factor using the ac-method.

- $-48 x^{2}-40 x+48$

A) $-8(3 x+2)(2 x-3)$
B) $-8(3 x-2)(2 x+3)$
C) $(-24 x+16)(2 x+3)$
D) prime

Question 74

Factor using the ac-method.

- $60 x^{2}+35 x y+5 y^{2}$

A) $5(3 x+y)(4 x+y)$
B) $(15 x+5 y)(4 x+y)$
C) $5(3 x-y)(4 x-y)$
D) prime

Question 75

Factor using the ac-method.

- $x^{5}-2 x^{4}-24 x^{3}$

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

Question 76

Factor using the ac-method.

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

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

Question 77

Determine whether the following is a trinomial square.

- $x^{2}+16 x+64$

Question 78

Determine whether the following is a trinomial square.

- $x^{2}-6 x y+9 y^{2}$

Question 79

Determine whether the following is a trinomial square.

- $x^{2}-10 x+100$

Question 80

Determine whether the following is a trinomial square.

- $27 x^{2}-117 x-90$