Question 1

Determine whether the following is a difference of squares.
-$16 x^{2}-23 y^{2}$

Accepted Answer

A) True 
 B)False

Question 2

Factor completely.
-$x^{10}+32 x^{5}+256$

Accepted Answer

A)  $\left(x^{5}-16\right)^{2}$ 
B)  $\left(x^{5}+16\right)\left(x^{5}-16\right)$ 
C)  Prime 
D)  $\left(x^{5}+16\right)^{2}$ 
A)  $\left(x^{5}-16\right)^{2}$ 
B)  $\left(x^{5}+16\right)\left(x^{5}-16\right)$ 
C)  Prime 
D)  $\left(x^{5}+16\right)^{2}$

Question 3

Factor.
-$3 y-12$

Accepted Answer

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

Question 4

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

Accepted Answer

A)  $(x-y)(3 x+9 y)$ 
B)  $3(x+y)(x-4 y)$ 
C)  $(3 x-3 y)(x+4 y)$ 
D)  $3(x-y)(x+4 y)$ 
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 5

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

Accepted Answer

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

Factor completely.
-$x^{2}-x-42$

Accepted Answer

A)  $(x+6)(x-7)$ 
B)  $(x+1)(x-13)$ 
C)  $(x-7)(x+7)$ 
D)  $(x+7)(x-6)$ 
A)  $(x+6)(x-7)$ 
B)  $(x+1)(x-13)$ 
C)  $(x-7)(x+7)$ 
D)  $(x+7)(x-6)$

Question 7

Factor completely.
-$4 x^{2}+9$

Accepted Answer

A)  $(2 x-3)^{2}$ 
B)  prime 
C)  $(2 x+3)^{2}$ 
D)  $(2 \mathrm{x}+3)(2 \mathrm{x}-3)$ 
A)  $(2 x-3)^{2}$ 
B)  prime 
C)  $(2 x+3)^{2}$ 
D)  $(2 \mathrm{x}+3)(2 \mathrm{x}-3)$

Question 8

Factor completely.
-$4 x^{3}+32 x^{2}+5 x+40$

Accepted Answer

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

Question 9

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

Accepted Answer

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)  $(3 z-4 y)(5 z+3 y)$ 
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 10

Solve the problem.
-The diagram below shows a rope connecting the top of a pole to the ground. The rope is $20 \mathrm{yd}$ long and touches the ground $15 \mathrm{yd}$ from the pole. How tall is the pole? Round approximations to the nearest tenth.

Accepted Answer

A)  87.5yd 
B)  $17.5 \mathrm{yd}$ 
C)  $6.6 \mathrm{yd}$ 
D)  $13.2 \mathrm{yd}$ 
A)  87.5yd 
B)  $17.5 \mathrm{yd}$ 
C)  $6.6 \mathrm{yd}$ 
D)  $13.2 \mathrm{yd}$

Question 11

Solve the problem.
-In a sports league of $n$ teams in which each team plays every other team twice, the total number $N$ of games to be played is given by $\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}$. How many teams are in a softball league if the total number of games played is 90 ?

Accepted Answer

A)  10 
B)  9 
C)  8 
D)  11 
A)  10 
B)  9 
C)  8 
D)  11

Question 12

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

Accepted Answer

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)  $12 x^{2} y^{2}\left(6 x^{7} y^{7}-2 x^{4} y^{2}-7\right)$ 
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 13

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

Accepted Answer

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)  $3 z^{2}\left(3 z^{3}-2\right)\left(4 z^{3}-3\right)$ 
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 14

Factor completely.
-$384 x^{2}-294 y^{2}$

Accepted Answer

A)  $(48 x-42 y)(8 x+7 y)$ 
B)  $6(8 x-7 y)(8 x+7 y)$ 
C)  $(8 x-7 y)(48 x+42 y)$ 
D)  $6(8 x+7 y)^{2}$ 
A)  $(48 x-42 y)(8 x+7 y)$ 
B)  $6(8 x-7 y)(8 x+7 y)$ 
C)  $(8 x-7 y)(48 x+42 y)$ 
D)  $6(8 x+7 y)^{2}$

Question 15

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

Accepted Answer

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)  $\left(x+\frac{3}{7}\right)^{2}$ 
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 16

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

Accepted Answer

A)  $6(3 x+2)(-2 x+3)$ 
B)  $6(-3 x+2)(2 x+3)$ 
C)  $(-3 x+2)(12 x+18)$ 
D)  $(-18 \mathrm{x}+12)(2 \mathrm{x}+3)$ 
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 17

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

Accepted Answer

A)  $(x-7 y)(x+3 y)$ 
B)  $(x-y)(x+3 y)$ 
C)  $(x+7 y)(x-3 y)$ 
D)  $(x-7 y)(x+y)$ 
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 18

Solve.
-Use the following graph to solve $x^{2}-2 x-8=0$.
$$y=x^{2}-2 x-8$$

Accepted Answer

A)  $-4,-2$ 
B)  $-2,4$ 
C)  $-4,2$ 
D)  4,2 
A)  $-4,-2$ 
B)  $-2,4$ 
C)  $-4,2$ 
D)  4,2

Question 19

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

Accepted Answer

A)  $2 a(a-4)(a-1)$ 
B)  $2 a(a-4)(a+1)$ 
C)  $2 a(a+4)(a-1)$ 
D)  $2 \mathrm{a}(\mathrm{a}+4)(\mathrm{a}+1)$ 
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 20

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

Accepted Answer

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)  $6\left(2 m^{9}-4 m^{7}+3 m^{5}\right)$ 
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)  $6\left(2 m^{9}-4 m^{7}+3 m^{5}\right)$

Determine whether the following is a difference of squares. - $16 x^{2}-23 y^{2}$

Factor completely. - $x^{10}+32 x^{5}+256$

Factor. - $3 y-12$

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

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

Factor completely. - $x^{2}-x-42$

Factor completely. - $4 x^{2}+9$

Factor completely. - $4 x^{3}+32 x^{2}+5 x+40$

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

Solve the problem. -In a sports league of $n$ teams in which each team plays every other team twice, the total number $N$ of games to be played is given by $\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}$ . How many teams are in a softball league if the total number of games played is 90 ?

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

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

Factor completely. - $384 x^{2}-294 y^{2}$

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

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

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

Solve. -Use the following graph to solve $x^{2}-2 x-8=0$ . $y=x^{2}-2 x-8$ $Solve. -Use the following graph to solve x^{2}-2 x-8=0 . y=x^{2}-2 x-8$

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

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

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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Equations of Lines and Simplifying Radical Expressions

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Exam 5: Polynomials: Factoring

Determine whether the following is a difference of squares. - 16x2−23y216 x^{2}-23 y^{2}16x2−23y2

Factor completely. - x10+32x5+256x^{10}+32 x^{5}+256x10+32x5+256

Factor. - 3y−123 y-123y−12

Factor. - 3x2−9xy−12y23 x^{2}-9 x y-12 y^{2}3x2−9xy−12y2

Factor. - b8−31bm6+29b3m8−37b8m6b^{8}-31 bm^{6}+29 b^{3} m^{8}-37 b^{8} m^{6}b8−31bm6+29b3m8−37b8m6

Factor completely. - x2−x−42x^{2}-x-42x2−x−42

Factor completely. - 4x2+94 x^{2}+94x2+9

Factor completely. - 4x3+32x2+5x+404 x^{3}+32 x^{2}+5 x+404x3+32x2+5x+40

Factor. - 15z2−11zy−12y215 z^{2}-11 z y-12 y^{2}15z2−11zy−12y2

Solve the problem. -The diagram below shows a rope connecting the top of a pole to the ground. The rope is 20yd20 \mathrm{yd}20yd long and touches the ground 15yd15 \mathrm{yd}15yd from the pole. How tall is the pole? Round approximations to the nearest tenth.

Solve the problem. -In a sports league of nnn teams in which each team plays every other team twice, the total number NNN of games to be played is given by N=n2−n\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}N=n2−n . How many teams are in a softball league if the total number of games played is 90 ?

Factor. - 72x9y9−24x6y4−84x2y272 x^{9} y 9-24 x^{6} y^{4}-84 x^{2} y^{2}72x9y9−24x6y4−84x2y2

Factor. - 36z8+51z5+18z236 z^{8}+51 z^{5}+18 z^{2}36z8+51z5+18z2

Factor completely. - 384x2−294y2384 x^{2}-294 y^{2}384x2−294y2

Factor. - x2+67x+949x^{2}+\frac{6}{7} x+\frac{9}{49}x2+76​x+499​

Factor. - −36x2−30x+36-36 x^{2}-30 x+36−36x2−30x+36

Factor. - x2−4xy−21y2x^{2}-4 x y-21 y^{2}x2−4xy−21y2

Solve. -Use the following graph to solve x2−2x−8=0x^{2}-2 x-8=0x2−2x−8=0 . y=x2−2x−8y=x^{2}-2 x-8y=x2−2x−8

Factor. - 2a3+6a2−8a2 a^{3}+6 a^{2}-8 a2a3+6a2−8a

Factor. - 12m9−24m7+18m512 m^{9}-24 m^{7}+18 m^{5}12m9−24m7+18m5