Question 1

Factor completely.
-$63 x^{2} y^{2}+30 x y-48$

Accepted Answer

A)  $(7 x y-8)(9 x y+6)$ 
B)  $(7 x y+8)(9 x y+6)$ 
C)  $(7 x y-8)(-9 x y-6)$ 
D)  $(7 x y+8)(9 x y-6)$ 
A)  $(7 x y-8)(9 x y+6)$ 
B)  $(7 x y+8)(9 x y+6)$ 
C)  $(7 x y-8)(-9 x y-6)$ 
D)  $(7 x y+8)(9 x y-6)$

Question 2

Factor by grouping.
-$x^{3}-3 x^{2}+4 x-12$

Accepted Answer

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)  $(x-3)\left(x^{2}+4\right)$ 
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 3

Factor completely.
-$20 x^{3}-54 x^{2}+10 x$

Accepted Answer

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

Question 4

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

Accepted Answer

A)  $(y+0.15)^{2}$ 
B)  $(y+0.6)(y-0.3)$ 
C)  $(y-0.6)(y+0.3)$ 
D)  $(y-0.6)(y-0.3)$ 
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 5

Factor using the ac-method.
-$x^{5}-2 x^{4}-24 x^{3}$

Accepted Answer

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)  $x^{3}(x+6)(x+4)$ 
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 6

Factor completely.
-$4 x^{3}+8 x^{2} y-32 x y^{2}$

Accepted Answer

A)  $4 x(x+2 y)(x-4 y)$ 
B)  $(x-2 y)\left(4 x^{2}+16 x y\right)$ 
C)  $4 x(x-2 y)(x+4 y)$ 
D)  $\left(4 x^{2}+8 x y\right)(x-4 y)$ 
A)  $4 x(x+2 y)(x-4 y)$ 
B)  $(x-2 y)\left(4 x^{2}+16 x y\right)$ 
C)  $4 x(x-2 y)(x+4 y)$ 
D)  $\left(4 x^{2}+8 x y\right)(x-4 y)$

Question 7

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

Accepted Answer

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)  $6(3 x-2)(x+5)$ 
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 8

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

Accepted Answer

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)  $2 m^{2}\left(6 m^{5}-3 m^{2}+7\right)$ 
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 9

Factor completely.
-$6 x^{2}+30 x-x y-5 y$

Accepted Answer

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

Question 10

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

Accepted Answer

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)  $(x-2)\left(3 x^{2}+12\right)$ 
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 11

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

Accepted Answer

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)  $(3 z-2 y)(3 z+4 y)$ 
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 12

Factor completely.
-$(\mathrm{m}+\mathrm{n})(\mathrm{x}+4)+(\mathrm{m}+\mathrm{n})(\mathrm{y}+6)$

Accepted Answer

A)  $(m+n+10)(x+y)$ 
B)  $(m+n+4)(x+y+6)$ 
C)  $(m+n)(x+y+10)$ 
D)  $(m+n)(2 x+10)$ 
A)  $(m+n+10)(x+y)$ 
B)  $(m+n+4)(x+y+6)$ 
C)  $(m+n)(x+y+10)$ 
D)  $(m+n)(2 x+10)$

Question 13

Factor completely.
-$49+14 x+x^{2}$

Accepted Answer

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

Question 14

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

Accepted Answer

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

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

Accepted Answer

A)  $(u+5 v)(u-8 v)$ 
B)  $(u-5 v)(u+v)$ 
C)  $(u-v)(u+8 v)$ 
D)  $(u-5 v)(u+8 v)$ 
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 16

Find the GCF.
-$2 x^{4}, 6 x^{2}$

Accepted Answer

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

Question 17

Determine whether the following is a trinomial square.
-$x^{2}-6 x y+9 y^{2}$

Accepted Answer

A) True 
 B)False

Question 18

Solve by factoring and using the principle of zero products.
-$6 d^{2}+13 d+6=0$

Accepted Answer

A)  $-\frac{3}{2},-\frac{2}{3}$ 
B)  $-\frac{2}{3},-\frac{2}{3}$ 
C)  $\frac{2}{3}, \frac{3}{2}$ 
D)  $\frac{3}{2}, \frac{2}{3}$ 
A)  $-\frac{3}{2},-\frac{2}{3}$ 
B)  $-\frac{2}{3},-\frac{2}{3}$ 
C)  $\frac{2}{3}, \frac{3}{2}$ 
D)  $\frac{3}{2}, \frac{2}{3}$

Question 19

Find the $x$-intercepts of the graph of the equation. (The grids are intentionally not included.) 179) $y=x^{2}-x-72$
-$y=x^{2}+2 x-35$

Accepted Answer

A)  $(7,0),(-5,0)$ 
B)  $(12,0)$ 
C)  $(-7,0),(5,0)$ 
D)  $(7,0),(1,0)$ 
A)  $(7,0),(-5,0)$ 
B)  $(12,0)$ 
C)  $(-7,0),(5,0)$ 
D)  $(7,0),(1,0)$

Question 20

Determine whether the following is a difference of squares.
-$x^{2}-9$

Accepted Answer

A) True 
 B)False

Factor completely. - $63 x^{2} y^{2}+30 x y-48$

Factor by grouping. - $x^{3}-3 x^{2}+4 x-12$

Factor completely. - $20 x^{3}-54 x^{2}+10 x$

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

Factor using the ac-method. - $x^{5}-2 x^{4}-24 x^{3}$

Factor completely. - $4 x^{3}+8 x^{2} y-32 x y^{2}$

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

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

Factor completely. - $6 x^{2}+30 x-x y-5 y$

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

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

Factor completely. - $(\mathrm{m}+\mathrm{n})(\mathrm{x}+4)+(\mathrm{m}+\mathrm{n})(\mathrm{y}+6)$

Factor completely. - $49+14 x+x^{2}$

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

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

Find the GCF. - $2 x^{4}, 6 x^{2}$

Determine whether the following is a trinomial square. - $x^{2}-6 x y+9 y^{2}$

Solve by factoring and using the principle of zero products. - $6 d^{2}+13 d+6=0$

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) 179) $y=x^{2}-x-72$ - $y=x^{2}+2 x-35$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) 179) y=x^{2}-x-72 - y=x^{2}+2 x-35$

Determine whether the following is a difference of squares. - $x^{2}-9$

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Fraction Notation

Decimal Notation

Percent Notation

Data, Graphs, and Statistics

Geometry

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

Systems of Equations

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Exam 11: Polynomials: Factoring

Factor completely. - 63x2y2+30xy−4863 x^{2} y^{2}+30 x y-4863x2y2+30xy−48

Factor by grouping. - x3−3x2+4x−12x^{3}-3 x^{2}+4 x-12x3−3x2+4x−12

Factor completely. - 20x3−54x2+10x20 x^{3}-54 x^{2}+10 x20x3−54x2+10x

Factor. - y2+0.3y−0.18y^{2}+0.3 y-0.18y2+0.3y−0.18

Factor using the ac-method. - x5−2x4−24x3x^{5}-2 x^{4}-24 x^{3}x5−2x4−24x3

Factor completely. - 4x3+8x2y−32xy24 x^{3}+8 x^{2} y-32 x y^{2}4x3+8x2y−32xy2

Factor. - 18x3−78x2−60x18 x^{3}-78 x^{2}-60 x18x3−78x2−60x

Factor. - 12m7−6m4+14m212 m^{7}-6 m^{4}+14 m^{2}12m7−6m4+14m2

Factor completely. - 6x2+30x−xy−5y6 x^{2}+30 x-x y-5 y6x2+30x−xy−5y

Factor. - 3x3+6x2−24x3 x^{3}+6 x^{2}-24 x3x3+6x2−24x

Factor. - 9z2+6zy−8y29 z^{2}+6 z y-8 y^{2}9z2+6zy−8y2

Factor completely. - (m+n)(x+4)+(m+n)(y+6)(\mathrm{m}+\mathrm{n})(\mathrm{x}+4)+(\mathrm{m}+\mathrm{n})(\mathrm{y}+6)(m+n)(x+4)+(m+n)(y+6)

Factor completely. - 49+14x+x249+14 x+x^{2}49+14x+x2

Factor. - x2+4xy−165y2x^{2}+4 x y-165 y^{2}x2+4xy−165y2

Factor. - u2−3uv−40v2u^{2}-3 u v-40 v^{2}u2−3uv−40v2

Find the GCF. - 2x4,6x22 x^{4}, 6 x^{2}2x4,6x2

Determine whether the following is a trinomial square. - x2−6xy+9y2x^{2}-6 x y+9 y^{2}x2−6xy+9y2

Solve by factoring and using the principle of zero products. - 6d2+13d+6=06 d^{2}+13 d+6=06d2+13d+6=0

Find the xxx -intercepts of the graph of the equation. (The grids are intentionally not included.) 179) y=x2−x−72y=x^{2}-x-72y=x2−x−72 - y=x2+2x−35y=x^{2}+2 x-35y=x2+2x−35

Determine whether the following is a difference of squares. - x2−9x^{2}-9x2−9