Question 1

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

Accepted Answer

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 
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 2

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

Accepted Answer

A)  $(x-0.4)(x+0.3)$ 
B)  $(x+0.4)(x-0.3)$ 
C)  $(x-0.4)(x-0.3)$ 
D)  $(x-0.35)^{2}$ 
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 3

Solve using the principle of zero products.
-$(x-0.5)(x+0.2)=0$

Accepted Answer

A)  $0.5,-0.2$ 
B)  $-0.5,0.2$ 
C)  $0.5,0.2$ 
D)  $0.5,-0.5,0.2,-0.2$ 
A)  $0.5,-0.2$ 
B)  $-0.5,0.2$ 
C)  $0.5,0.2$ 
D)  $0.5,-0.5,0.2,-0.2$

Question 4

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

Accepted Answer

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)  $(4 x+y)(x+9 y)$ 
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 5

Factor completely.
-$50 x^{2}-98$

Accepted Answer

A)  $(5 x+7)(10 x-14)$ 
B)  $2(5 x+7)(5 x-7)$ 
C)  $2(5 x-7)^{2}$ 
D)  $(10 x+14)(5 x-7)$ 
A)  $(5 x+7)(10 x-14)$ 
B)  $2(5 x+7)(5 x-7)$ 
C)  $2(5 x-7)^{2}$ 
D)  $(10 x+14)(5 x-7)$

Question 6

Factor by grouping.
-$x^{3}+5 x^{2}+3 x+15$

Accepted Answer

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)  $(x+5)\left(x^{2}+3\right)$ 
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 7

Solve the problem.
-Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 18 miles, the distance between the cars was 6 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?

Accepted Answer

A)  36 miles 
B)  24 miles 
C)  18 miles 
D)  30 miles 
A)  36 miles 
B)  24 miles 
C)  18 miles 
D)  30 miles

Question 8

Factor by grouping.
-$8 x^{2}+6 x-12 x-9$

Accepted Answer

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

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

Accepted Answer

A)  $(x+2)(6 x-18)$ 
B)  $6(x+2)(x-3)$ 
C)  $6(x-2)(x+3)$ 
D)  $(6 x+12)(x-3)$ 
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 10

Find the $x$-intercepts of the graph of the equation. (The grids are intentionally not included.) 179) $y=x^{2}-x-72$
-$y=x^{2}+3 x-18$

Accepted Answer

A)  $\left(-\frac{7}{2}, 0\right),(2,0)$ 
B)  $(-6,0),(3,0)$ 
C)  $(0,-18)$ 
D)  $(-7,0),(4,0)$ 
A)  $\left(-\frac{7}{2}, 0\right),(2,0)$ 
B)  $(-6,0),(3,0)$ 
C)  $(0,-18)$ 
D)  $(-7,0),(4,0)$

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 $\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}$. What is the total number of games to be played in a football league having 17 teams?

Accepted Answer

A)  289 
B)  272 
C)  34 
D)  306 
A)  289 
B)  272 
C)  34 
D)  306

Question 12

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 - x - 72

Accepted Answer

A)  $(72,0)$ 
B)  $(9,0),(8,0)$ 
C)  $(-8,0),(9,0)$ 
D)  $(1,0),(-72,0)$ 
A)  $(72,0)$ 
B)  $(9,0),(8,0)$ 
C)  $(-8,0),(9,0)$ 
D)  $(1,0),(-72,0)$

Question 13

Determine whether the following is a difference of squares.
-$x^{2}+36$

Accepted Answer

A) True 
 B)False

Question 14

Factor completely.
-$98 x^{2}-50 y^{2}$

Accepted Answer

A)  $2(7 x-5 y)^{2}$ 
B)  $(14 x+10 y)(7 x-5 y)$ 
C)  $(7 x+5 y)(14 x-10 y)$ 
D)  $2(7 x+5 y)(7 x-5 y)$ 
A)  $2(7 x-5 y)^{2}$ 
B)  $(14 x+10 y)(7 x-5 y)$ 
C)  $(7 x+5 y)(14 x-10 y)$ 
D)  $2(7 x+5 y)(7 x-5 y)$

Question 15

Solve the problem.
-Below is a diagram of a water slide. The slide is 24 ft long. The ladder leading to the slide is 18 ft long. How far is it from the end of the slide to the foot of the ladder? Round approximations to the nearest tenth.

Accepted Answer

A)  $126 \mathrm{ft}$ 
B)  $15.9 \mathrm{ft}$ 
C)  $8 \mathrm{ft}$ 
D)  $21 \mathrm{ft}$ 
A)  $126 \mathrm{ft}$ 
B)  $15.9 \mathrm{ft}$ 
C)  $8 \mathrm{ft}$ 
D)  $21 \mathrm{ft}$

Question 16

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

Accepted Answer

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)  $(12 x+8 y)(3 x+2 y)$ 
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 17

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

Accepted Answer

A)  $(5 x-6)(2 x+3)$ 
B)  $(10 x-6)(x+3)$ 
C)  $(10 x+6)(x-3)$ 
D)  $(5 x+6)(2 x-3)$ 
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 18

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

Accepted Answer

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

Question 19

Solve by factoring and using the principle of zero products.
-$3 x^{2}-15 x+18=0$

Accepted Answer

A)  $0,2,3$ 
B)  $3,2,3$ 
C)  2,3 
D)  $-2,-3$ 
A)  $0,2,3$ 
B)  $3,2,3$ 
C)  2,3 
D)  $-2,-3$

Question 20

Factor completely.
-$36 x^{2}+84 x+49$

Accepted Answer

A)  $(6 x+7)^{2}$ 
B)  $(6 x-7)^{2}$ 
C)  $(6 x+7)(6 x-7)$ 
D)  Prime 
A)  $(6 x+7)^{2}$ 
B)  $(6 x-7)^{2}$ 
C)  $(6 x+7)(6 x-7)$ 
D)  Prime

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

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

Solve using the principle of zero products. - $(x-0.5)(x+0.2)=0$

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

Factor completely. - $50 x^{2}-98$

Factor by grouping. - $x^{3}+5 x^{2}+3 x+15$

Solve the problem. -Two cars leave an intersection. One car travels north; the other east. When the car traveling north had gone 18 miles, the distance between the cars was 6 miles more than the distance traveled by the car heading east. How far had the eastbound car traveled?

Factor by grouping. - $8 x^{2}+6 x-12 x-9$

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

Find the $x$ -intercepts of the graph of the equation. (The grids are intentionally not included.) 179) $y=x^{2}-x-72$ - $y=x^{2}+3 x-18$ $Find the x -intercepts of the graph of the equation. (The grids are intentionally not included.) 179) y=x^{2}-x-72 - y=x^{2}+3 x-18$

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 $\mathrm{N}=\mathrm{n}^{2}-\mathrm{n}$ . What is the total number of games to be played in a football league having 17 teams?

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

Determine whether the following is a difference of squares. - $x^{2}+36$

Factor completely. - $98 x^{2}-50 y^{2}$

Solve the problem. -Below is a diagram of a water slide. The slide is 24 ft long. The ladder leading to the slide is 18 ft long. How far is it from the end of the slide to the foot of the ladder? Round approximations to the nearest tenth.

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

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

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

Solve by factoring and using the principle of zero products. - $3 x^{2}-15 x+18=0$

Factor completely. - $36 x^{2}+84 x+49$

Whole Numbers

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

Radical Expressions and Equations

Quadratic Equations

Converting Units of Measurement

Filters

Exam 11: Polynomials: Factoring

Factor. - 72x7y9+60x5y5+36x2y272 x^{7} y^{9}+60 x^{5} y^{5}+36 x^{2} y^{2}72x7y9+60x5y5+36x2y2

Factor. - x2−0.7x+0.12x^{2}-0.7 x+0.12x2−0.7x+0.12

Solve using the principle of zero products. - (x−0.5)(x+0.2)=0(x-0.5)(x+0.2)=0(x−0.5)(x+0.2)=0

Factor. - 4x2+12xy+9y24 x^{2}+12 x y+9 y^{2}4x2+12xy+9y2

Factor completely. - 50x2−9850 x^{2}-9850x2−98

Factor by grouping. - x3+5x2+3x+15x^{3}+5 x^{2}+3 x+15x3+5x2+3x+15