Question 1

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

Accepted Answer

A)  $\mathrm{t}(8-\mathrm{m})+\mathrm{s}$ 
B)  No common factor 
C)  $(\mathrm{t}-\mathrm{s})(8-\mathrm{m})$ 
D)  $(\mathrm{t}+\mathrm{s})(8-\mathrm{m})$ 
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 2

Solve.
-Use the following graph to solve $x^{2}+2 x-15=0$.
Y = x2 + 2x - 15

Accepted Answer

A)  $-3,5$ 
B)  $-5,3$ 
C)  3,5 
D)  $-5,-3$ 
A)  $-3,5$ 
B)  $-5,3$ 
C)  3,5 
D)  $-5,-3$

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

Question 5

Factor completely.
-$128 x^{2}-50$

Accepted Answer

A)  $(8 x+5)(16 x-10)$ 
B)  $2(8 x-5)^{2}$ 
C)  $2(8 x+5)(8 x-5)$ 
D)  $(16 x+10)(8 x-5)$ 
A)  $(8 x+5)(16 x-10)$ 
B)  $2(8 x-5)^{2}$ 
C)  $2(8 x+5)(8 x-5)$ 
D)  $(16 x+10)(8 x-5)$

Question 6

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

Accepted Answer

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)  $(2 x+3 y)(3 x-2 y)$ 
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 7

Solve the problem.
-In a sports league of $\mathrm{n}$ teams in which each team plays every other team twice, the total number $\mathrm{N}$ 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 110 ?

Accepted Answer

A)  10 
B)  11 
C)  9 
D)  12 
A)  10 
B)  11 
C)  9 
D)  12

Question 8

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

Accepted Answer

A)  $(x-7 y)(x+y)$ 
B)  $(x+7 y)(x-3 y)$ 
C)  $(x-7 y)(x+3 y)$ 
D)  $(x-y)(x+3 y)$ 
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 9

Factor completely.
-$x^{2}+20 x+100$

Accepted Answer

A)  Prime 
B)  $(x+10)(x-10)$ 
C)  $(x+10)^{2}$ 
D)  $(x-10)^{2}$ 
A)  Prime 
B)  $(x+10)(x-10)$ 
C)  $(x+10)^{2}$ 
D)  $(x-10)^{2}$

Question 10

Factor completely.
-$4 x^{2}-81$

Accepted Answer

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

Question 11

Solve the problem.
-The height of a triangle is $4 \mathrm{~cm}$ more than the length of the base. If the area of the triangle is $126 \mathrm{~cm}^{2}$, find the height and length of the base.

Accepted Answer

A)  height: $14 \mathrm{~cm}$; base: $10 \mathrm{~cm}$ 
B)  height: $19 \mathrm{~cm}$; base: $13 \mathrm{~cm}$ 
C)  height: $18 \mathrm{~cm}$; base: $14 \mathrm{~cm}$ 
D)  height: $17 \mathrm{~cm}$; base: $13 \mathrm{~cm}$ 
A)  height: $14 \mathrm{~cm}$; base: $10 \mathrm{~cm}$ 
B)  height: $19 \mathrm{~cm}$; base: $13 \mathrm{~cm}$ 
C)  height: $18 \mathrm{~cm}$; base: $14 \mathrm{~cm}$ 
D)  height: $17 \mathrm{~cm}$; base: $13 \mathrm{~cm}$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

A)  Prime 
B)  $(2 x+3 t)(3 x-2 t)$ 
C)  $(6 x+3 t)(x-2 t)$ 
D)  $(2 x-3 t)(3 x+2 t)$ 
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 15

Solve the problem.
-A rectangular garden is three times as long as it is wide. If the area of the garden is $768 \mathrm{ft}^{2}$, find the length and width of the garden.

Accepted Answer

A)  length: $45 \mathrm{ft}$; width: $15 \mathrm{ft}$ 
B)  length: $256 \mathrm{ft}$; width: $3 \mathrm{ft}$ 
C)  length: $48 \mathrm{ft}$; width: $16 \mathrm{ft}$ 
D)  length: $16 \mathrm{ft}$; width: $\frac{16}{3} \mathrm{ft}$ 
A)  length: $45 \mathrm{ft}$; width: $15 \mathrm{ft}$ 
B)  length: $256 \mathrm{ft}$; width: $3 \mathrm{ft}$ 
C)  length: $48 \mathrm{ft}$; width: $16 \mathrm{ft}$ 
D)  length: $16 \mathrm{ft}$; width: $\frac{16}{3} \mathrm{ft}$

Question 16

Factor completely.
-$4 \mathrm{~m}^{2}-\frac{9}{4}$

Accepted Answer

A)  $\left(2 \mathrm{~m}-\frac{3}{2}\right)^{2}$ 
B)  $\left(2 m+\frac{3}{2}\right)\left(2 m-\frac{3}{2}\right)$ 
C)  $\left(2 \mathrm{~m}+\frac{3}{2}\right)^{2}$ 
D)  Prime 
A)  $\left(2 \mathrm{~m}-\frac{3}{2}\right)^{2}$ 
B)  $\left(2 m+\frac{3}{2}\right)\left(2 m-\frac{3}{2}\right)$ 
C)  $\left(2 \mathrm{~m}+\frac{3}{2}\right)^{2}$ 
D)  Prime

Question 17

Solve the problem.
-The product of two consecutive integers is 11 more than their sum. Find the integers.

Accepted Answer

A)  -3 and -2 
B)  4 and 5 
C)  4,5 or $-3,-2$ 
D)  3,4 or $-3,-2$ 
A)  -3 and -2 
B)  4 and 5 
C)  4,5 or $-3,-2$ 
D)  3,4 or $-3,-2$

Question 18

Solve the problem.
-A long-distance runner runs 2 miles south and then 4 miles east. How far is the runner from the starting point? Round to nearest tenth.

Accepted Answer

A)  $2.5 \mathrm{mi}$ 
B)  $1.5 \mathrm{mi}$ 
C)  $4.5 \mathrm{mi}$ 
D)  $1.1 \mathrm{mi}$ 
A)  $2.5 \mathrm{mi}$ 
B)  $1.5 \mathrm{mi}$ 
C)  $4.5 \mathrm{mi}$ 
D)  $1.1 \mathrm{mi}$

Question 19

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

Accepted Answer

A)  $2 x(x-2)(x+5)$ 
B)  Prime 
C)  $2 x(x+2)(x-5)$ 
D)  $\left(2 x^{2}+4 x\right)(x-5)$ 
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 20

Solve the problem.
-A number is 12 less than its square. Find all such numbers.

Accepted Answer

A)  -3 and 3 
B)  -3 and 4 
C)  -4 and 4 
D)  -4 and 3 
A)  -3 and 3 
B)  -3 and 4 
C)  -4 and 4 
D)  -4 and 3

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

Solve. -Use the following graph to solve $x^{2}+2 x-15=0$ . Y = x² + 2x - 15 $Solve. -Use the following graph to solve x^{2}+2 x-15=0 . Y = x<sup>2</sup> + 2x - 15$

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

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

Factor completely. - $128 x^{2}-50$

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

Solve the problem. -In a sports league of $\mathrm{n}$ teams in which each team plays every other team twice, the total number $\mathrm{N}$ 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 110 ?

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

Factor completely. - $x^{2}+20 x+100$

Factor completely. - $4 x^{2}-81$

Solve the problem. -The height of a triangle is $4 \mathrm{~cm}$ more than the length of the base. If the area of the triangle is $126 \mathrm{~cm}^{2}$ , find the height and length of the base.

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

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

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

Solve the problem. -A rectangular garden is three times as long as it is wide. If the area of the garden is $768 \mathrm{ft}^{2}$ , find the length and width of the garden.

Factor completely. - $4 \mathrm{~m}^{2}-\frac{9}{4}$

Solve the problem. -The product of two consecutive integers is 11 more than their sum. Find the integers.

Solve the problem. -A long-distance runner runs 2 miles south and then 4 miles east. How far is the runner from the starting point? Round to nearest tenth.

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

Solve the problem. -A number is 12 less than its square. Find all such numbers.

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

Solve. -Use the following graph to solve x2+2x−15=0x^{2}+2 x-15=0x2+2x−15=0 . Y = x2 + 2x - 15

Factor. - t2+1.4t+0.49t^{2}+1.4 t+0.49t2+1.4t+0.49

Factor. - 10z2−7z−1210 z^{2}-7 z-1210z2−7z−12

Factor completely. - 128x2−50128 x^{2}-50128x2−50

Factor. - 6x2−13xy+6y26 x^{2}-13 x y+6 y^{2}6x2−13xy+6y2

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

Factor completely. - x2+20x+100x^{2}+20 x+100x2+20x+100

Factor completely. - 4x2−814 x^{2}-814x2−81

Solve the problem. -The height of a triangle is 4 cm4 \mathrm{~cm}4 cm more than the length of the base. If the area of the triangle is 126 cm2126 \mathrm{~cm}^{2}126 cm2 , find the height and length of the base.

Factor. - 4x2−5x+94 x^{2}-5 x+94x2−5x+9

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

Factor. - 6x2+5xt−6t26 x^{2}+5 x t-6 t^{2}6x2+5xt−6t2

Solve the problem. -A rectangular garden is three times as long as it is wide. If the area of the garden is 768ft2768 \mathrm{ft}^{2}768ft2 , find the length and width of the garden.

Factor completely. - 4 m2−944 \mathrm{~m}^{2}-\frac{9}{4}4 m2−49​