Question 1

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

Accepted Answer

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

Solve.
-Use the following graph to solve $x^{2}+4 x-5=0$.
Y = x2 + 4x - 5

Accepted Answer

A)  $-1,5$ 
B)  $-5,-1$ 
C)  5,1 
D)  $-5,1$ 
A)  $-1,5$ 
B)  $-5,-1$ 
C)  5,1 
D)  $-5,1$

Question 3

Solve the problem.
-Within a group of $n$ people, the number of possible handshakes, $N$, is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$. How many handshakes are possible at a meeting if 30 people are present?

Accepted Answer

A)  420 
B)  870 
C)  435 
D)  465 
A)  420 
B)  870 
C)  435 
D)  465

Question 4

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

Accepted Answer

A)  $(8 m-9 n)(9-m)$ 
B)  No common factor 
C)  $(8 m+9 n)(9-m)$ 
D)  $m(8+9 n)(9-1)$ 
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 5

Factor completely.
-$36 y^{4}-49$

Accepted Answer

A)  $\left(6 y^{2}+7\right)\left(6 y^{2}-7\right)$ 
B)  $\left(6 y^{2}+7\right)^{2}$ 
C)  $\left(6 y^{2}-7\right)^{2}$ 
D)  Prime 
A)  $\left(6 y^{2}+7\right)\left(6 y^{2}-7\right)$ 
B)  $\left(6 y^{2}+7\right)^{2}$ 
C)  $\left(6 y^{2}-7\right)^{2}$ 
D)  Prime

Question 6

Solve the problem.
-Within a group of $n$ people, the number of possible handshakes, $N$, is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$. At a party, everybody shakes hands with every other person. If the total number of handshakes is 253 , how many people are at the party?

Accepted Answer

A)  24 
B)  22 
C)  25 
D)  23 
A)  24 
B)  22 
C)  25 
D)  23

Question 7

Solve.
-Use the following graph to solve $x^{2}-3 x-10=0$. y = x2 - 3x - 10

Accepted Answer

A)  $-5,-2$ 
B)  $-2,5$ 
C)  2,5 
D)  $-5,2$ 
A)  $-5,-2$ 
B)  $-2,5$ 
C)  2,5 
D)  $-5,2$

Question 8

Solve the problem.
-If an object is dropped, the distance it falls is given by $\mathrm{d}=16 \mathrm{t}^{2}$. Find the distance an object would fall in 8 seconds.

Accepted Answer

A)  $128 \mathrm{ft}$ 
B)  $1024 \mathrm{ft}$ 
C)  $512 \mathrm{ft}$ 
D)  $2048 \mathrm{ft}$ 
A)  $128 \mathrm{ft}$ 
B)  $1024 \mathrm{ft}$ 
C)  $512 \mathrm{ft}$ 
D)  $2048 \mathrm{ft}$

Question 9

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

Accepted Answer

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

Question 10

Solve the problem.
-The diagram below shows a rope connecting the top of a pole to the ground. The rope is 30 yd long and touches the ground 25 yd from the pole. How tall is the pole? Round approximations to the nearest tenth.

Accepted Answer

A)  $27.5 \mathrm{yd}$ 
B)  $137.5 \mathrm{yd}$ 
C)  $8.3 \mathrm{yd}$ 
D)  16.6 yd 
A)  $27.5 \mathrm{yd}$ 
B)  $137.5 \mathrm{yd}$ 
C)  $8.3 \mathrm{yd}$ 
D)  16.6 yd

Question 11

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

Accepted Answer

A)  $5(3 x+2)(-2 x+3)$ 
B)  $(-15 x+10)(2 x+3)$ 
C)  $5(-3 x+2)(2 x+3)$ 
D)  $(-3 x+2)(10 x+15)$ 
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 12

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

Accepted Answer

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

Question 13

Determine whether the following is a trinomial square.
-$x^{2}-10 x+100$

Accepted Answer

A) True 
 B)False

Question 14

Solve using the principle of zero products.
-$(x-3)(x+7)=0$

Accepted Answer

A)  $-3,7$ 
B)  3,7 
C)  $3,-3,7,-7$ 
D)  $3,-7$ 
A)  $-3,7$ 
B)  3,7 
C)  $3,-3,7,-7$ 
D)  $3,-7$

Question 15

Solve by factoring and using the principle of zero products.
-$25 b^{2}+35 b-6=-18$

Accepted Answer

A)  $-\frac{5}{4},-\frac{3}{5}$ 
B)  $\frac{5}{4}, \frac{5}{3}$ 
C)  $-\frac{4}{5},-\frac{3}{5}$ 
D)  $\frac{4}{5}, \frac{3}{5}$ 
A)  $-\frac{5}{4},-\frac{3}{5}$ 
B)  $\frac{5}{4}, \frac{5}{3}$ 
C)  $-\frac{4}{5},-\frac{3}{5}$ 
D)  $\frac{4}{5}, \frac{3}{5}$

Question 16

Factor completely.
-$2 x^{2}\left(p+q^{3}\right)-\left(p+q^{3}\right)$

Accepted Answer

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

Question 17

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

Accepted Answer

A)  $3 x^{2} y^{6}(y+3)$ 
B)  $3 x^{6} y^{2}(y+3)$ 
C)  $y+3$ 
D)  $x^{2} y^{6}(3 y+3)$ 
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 18

Factor completely.
-$6 a^{3}+9 a^{2} b-8 a b^{2}-12 b^{3}$

Accepted Answer

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

Question 19

Factor completely.
-$98 a^{4} b-72 b^{3}$

Accepted Answer

A)  $2 b(7 a+6 b)^{2}$ 
B)  Prime 
C)  $2 b\left(7 a^{2}+6 b\right)\left(7 a^{2}-6 b\right)$ 
D)  $2 b(7 a-6 b)^{2}$ 
A)  $2 b(7 a+6 b)^{2}$ 
B)  Prime 
C)  $2 b\left(7 a^{2}+6 b\right)\left(7 a^{2}-6 b\right)$ 
D)  $2 b(7 a-6 b)^{2}$

Question 20

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

Accepted Answer

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

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

Solve. -Use the following graph to solve $x^{2}+4 x-5=0$ . Y = x² + 4x - 5 $Solve. -Use the following graph to solve x^{2}+4 x-5=0 . Y = x<sup>2</sup> + 4x - 5$

Solve the problem. -Within a group of $n$ people, the number of possible handshakes, $N$ , is given by $\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)$ . How many handshakes are possible at a meeting if 30 people are present?

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

Factor completely. - $36 y^{4}-49$

Solve. -Use the following graph to solve $x^{2}-3 x-10=0$ . y = x² - 3x - 10 $Solve. -Use the following graph to solve x^{2}-3 x-10=0 . y = x<sup>2</sup> - 3x - 10$

Solve the problem. -If an object is dropped, the distance it falls is given by $\mathrm{d}=16 \mathrm{t}^{2}$ . Find the distance an object would fall in 8 seconds.

Solve. -Use the following graph to solve $x^{2}-2 x-8=0$ . Y = x² - 2x - 8 $Solve. -Use the following graph to solve x^{2}-2 x-8=0 . Y = x<sup>2</sup> - 2x - 8$

Solve the problem. -The diagram below shows a rope connecting the top of a pole to the ground. The rope is 30 yd long and touches the ground 25 yd from the pole. How tall is the pole? Round approximations to the nearest tenth.

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

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

Determine whether the following is a trinomial square. - $x^{2}-10 x+100$

Solve using the principle of zero products. - $(x-3)(x+7)=0$

Solve by factoring and using the principle of zero products. - $25 b^{2}+35 b-6=-18$

Factor completely. - $2 x^{2}\left(p+q^{3}\right)-\left(p+q^{3}\right)$

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

Factor completely. - $6 a^{3}+9 a^{2} b-8 a b^{2}-12 b^{3}$

Factor completely. - $98 a^{4} b-72 b^{3}$

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

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. - 8y2+36y−208 y^{2}+36 y-208y2+36y−20

Solve. -Use the following graph to solve x2+4x−5=0x^{2}+4 x-5=0x2+4x−5=0 . Y = x2 + 4x - 5

Solve the problem. -Within a group of nnn people, the number of possible handshakes, NNN , is given by N=12(n2−n)\mathrm{N}=\frac{1}{2}\left(\mathrm{n}^{2}-\mathrm{n}\right)N=21​(n2−n) . How many handshakes are possible at a meeting if 30 people are present?

Factor. - 8m(9−m)+9n(9−m)8 m(9-m)+9 n(9-m)8m(9−m)+9n(9−m)

Factor completely. - 36y4−4936 y^{4}-4936y4−49

Solve. -Use the following graph to solve x2−3x−10=0x^{2}-3 x-10=0x2−3x−10=0 . y = x2 - 3x - 10

Solve the problem. -If an object is dropped, the distance it falls is given by d=16t2\mathrm{d}=16 \mathrm{t}^{2}d=16t2 . Find the distance an object would fall in 8 seconds.

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