Question 1

Solve the problem.
-The product of two consecutive integers is 71 more than their sum. Find the integers.

Accepted Answer

A)  9 and 10 
B)  -8 and -7 
C)  8,9 or $-8,-7$ 
D)  9,10 or $-8,-7$ 
A)  9 and 10 
B)  -8 and -7 
C)  8,9 or $-8,-7$ 
D)  9,10 or $-8,-7$

Question 2

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

Question 3

Solve by factoring and using the principle of zero products.
-$12 b^{2}+28 b+12=-3$

Accepted Answer

A)  $\frac{6}{5}, \frac{2}{3}$ 
B)  $\frac{5}{6}, \frac{3}{2}$ 
C)  $-\frac{5}{6},-\frac{3}{2}$ 
D)  $-\frac{6}{5},-\frac{3}{2}$ 
A)  $\frac{6}{5}, \frac{2}{3}$ 
B)  $\frac{5}{6}, \frac{3}{2}$ 
C)  $-\frac{5}{6},-\frac{3}{2}$ 
D)  $-\frac{6}{5},-\frac{3}{2}$

Question 4

Factor.
-$3 x^{4}-18 x^{3}+24 x^{2}$

Accepted Answer

A)  $3 x^{2}(x-4)(x-2)$ 
B)  $3 x^{2}(x-4)(x+2)$ 
C)  $3 x^{2}(x+4)(x+2)$ 
D)  $3 x^{2}(x+4)(x-2)$ 
A)  $3 x^{2}(x-4)(x-2)$ 
B)  $3 x^{2}(x-4)(x+2)$ 
C)  $3 x^{2}(x+4)(x+2)$ 
D)  $3 x^{2}(x+4)(x-2)$

Question 5

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

Accepted Answer

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

Question 6

Factor.
-$45 x^{2}+60 x y+20 y^{2}$

Accepted Answer

A)  $5\left(9 x^{2}+12 x y+4 y\right)$ 
B)  $5(3 x-2 y)(3 x+2 y)$ 
C)  $5(3 x+2 y)^{2}$ 
D)  $(15 x+10 y)(3 x+2 y)$ 
A)  $5\left(9 x^{2}+12 x y+4 y\right)$ 
B)  $5(3 x-2 y)(3 x+2 y)$ 
C)  $5(3 x+2 y)^{2}$ 
D)  $(15 x+10 y)(3 x+2 y)$

Question 7

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

Accepted Answer

A) True 
 B)False

Question 8

Factor completely.
-$64 \mathrm{x}-25 \mathrm{x}^{3}$

Accepted Answer

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

Question 9

Factor using the ac-method.
-$-30 x^{2}-25 x+30$

Accepted Answer

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

Question 10

Factor.
-$x^{3}-x^{2}-30 x$

Accepted Answer

A)  Prime 
B)  $x(x+5)(x-6)$ 
C)  $\left(x^{2}+1\right)(x-30)$ 
D)  $x(x+6)(x-5)$ 
A)  Prime 
B)  $x(x+5)(x-6)$ 
C)  $\left(x^{2}+1\right)(x-30)$ 
D)  $x(x+6)(x-5)$

Question 11

Find the GCF.
-$x^{7} y^{7}, x^{6} y^{5}, x^{6} y^{6},-x^{2} y^{2}$

Accepted Answer

A)  $x^{2} y^{2}$ 
B)  $x^{6} y^{5}$ 
C)  $-\mathrm{xy}$ 
D)  $x^{5} y^{5}$ 
A)  $x^{2} y^{2}$ 
B)  $x^{6} y^{5}$ 
C)  $-\mathrm{xy}$ 
D)  $x^{5} y^{5}$

Question 12

Solve by factoring and using the principle of zero products.
-$5 x^{2}-40 x+75=0$

Accepted Answer

A)  $-3,-5$ 
B)  $0,3,5$ 
C)  5, 3, 5 
D)  3, 5 
A)  $-3,-5$ 
B)  $0,3,5$ 
C)  5, 3, 5 
D)  3, 5

Question 13

Solve using the principle of zero products.
-$(x-3)(x+74)(2 x+14)=0$

Accepted Answer

A)  $-3,74,7$ 
B)  $3,-74,-\frac{1}{7}$ 
C)  $3,-74,-28$ 
D)  $3,-74,-7$ 
A)  $-3,74,7$ 
B)  $3,-74,-\frac{1}{7}$ 
C)  $3,-74,-28$ 
D)  $3,-74,-7$

Question 14

Solve the problem.
-If an object is dropped, the distance it falls is given by $d=16 t^{2}$. Find the distance an object would fall in 6 seconds.

Accepted Answer

A)  $576 \mathrm{ft}$ 
B)  $1152 \mathrm{ft}$ 
C)  $288 \mathrm{ft}$ 
D)  $96 \mathrm{ft}$ 
A)  $576 \mathrm{ft}$ 
B)  $1152 \mathrm{ft}$ 
C)  $288 \mathrm{ft}$ 
D)  $96 \mathrm{ft}$

Question 15

Factor completely.
-$-36 x^{3}-33 x^{2}+45 x$

Accepted Answer

A)  $x(-12 x+9)(3 x+5)$ 
B)  $x(4 x-3)(-9 x-15)$ 
C)  $-3\left(4 x^{2}-3\right)(3 x+5)$ 
D)  $-3 x(4 x-3)(3 x+5)$ 
A)  $x(-12 x+9)(3 x+5)$ 
B)  $x(4 x-3)(-9 x-15)$ 
C)  $-3\left(4 x^{2}-3\right)(3 x+5)$ 
D)  $-3 x(4 x-3)(3 x+5)$

Question 16

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

Accepted Answer

A)  $\left(x^{2}-9\right)(x+3)(x-3)$ 
B)  $\left(x^{2}+9\right)(x+3)(x-3)$ 
C)  $(x+3)^{2}(x-3)^{2}$ 
D)  Prime 
A)  $\left(x^{2}-9\right)(x+3)(x-3)$ 
B)  $\left(x^{2}+9\right)(x+3)(x-3)$ 
C)  $(x+3)^{2}(x-3)^{2}$ 
D)  Prime

Question 17

Factor completely.
-$6 x^{2}\left(p+q^{2}\right)-\left(p+q^{2}\right)$

Accepted Answer

A)  $\left(6-x^{2}\right)\left(p+q^{2}\right)$ 
B)  $\left(6 x^{2}-1\right)(p+q)^{2}$ 
C)  $6 x^{2}\left(p+q^{2}-1\right)$ 
D)  $\left(p+q^{2}\right)\left(6 x^{2}-1\right)$ 
A)  $\left(6-x^{2}\right)\left(p+q^{2}\right)$ 
B)  $\left(6 x^{2}-1\right)(p+q)^{2}$ 
C)  $6 x^{2}\left(p+q^{2}-1\right)$ 
D)  $\left(p+q^{2}\right)\left(6 x^{2}-1\right)$

Question 18

Solve by factoring and using the principle of zero products.
-$28 n^{2}+56 n=0$

Accepted Answer

A)  $-2,0$ 
B)  $-2,56$ 
C)  0 
D)  - 2 
A)  $-2,0$ 
B)  $-2,56$ 
C)  0 
D)  - 2

Question 19

Determine whether the following is a difference of squares.
-$x^{2}-49$

Accepted Answer

A) True 
 B)False

Question 20

Factor completely.
-$9 x^{2}+18 x+8$

Accepted Answer

A)  $(3 x-2)(3 x-4)$ 
B)  $(3 x+2)(3 x+4)$ 
C)  $(9 x+2)(x+4)$ 
D)  $(9 \mathrm{x}+1)(\mathrm{x}+8)$ 
A)  $(3 x-2)(3 x-4)$ 
B)  $(3 x+2)(3 x+4)$ 
C)  $(9 x+2)(x+4)$ 
D)  $(9 \mathrm{x}+1)(\mathrm{x}+8)$

Solve the problem. -The product of two consecutive integers is 71 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.

Solve by factoring and using the principle of zero products. - $12 b^{2}+28 b+12=-3$

Factor. - $3 x^{4}-18 x^{3}+24 x^{2}$

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

Factor. - $45 x^{2}+60 x y+20 y^{2}$

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

Factor completely. - $64 \mathrm{x}-25 \mathrm{x}^{3}$

Factor using the ac-method. - $-30 x^{2}-25 x+30$

Factor. - $x^{3}-x^{2}-30 x$

Find the GCF. - $x^{7} y^{7}, x^{6} y^{5}, x^{6} y^{6},-x^{2} y^{2}$

Solve by factoring and using the principle of zero products. - $5 x^{2}-40 x+75=0$

Solve using the principle of zero products. - $(x-3)(x+74)(2 x+14)=0$

Solve the problem. -If an object is dropped, the distance it falls is given by $d=16 t^{2}$ . Find the distance an object would fall in 6 seconds.

Factor completely. - $-36 x^{3}-33 x^{2}+45 x$

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

Factor completely. - $6 x^{2}\left(p+q^{2}\right)-\left(p+q^{2}\right)$

Solve by factoring and using the principle of zero products. - $28 n^{2}+56 n=0$

Determine whether the following is a difference of squares. - $x^{2}-49$

Factor completely. - $9 x^{2}+18 x+8$

Introduction to Real Numbers and Algebraic Expressions

Solving Equations and Inequalities

Graphs of Linear Equations

Polynomials: Operations

Rational Expressions and Equations

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Exam 5: Polynomials: Factoring

Solve the problem. -The product of two consecutive integers is 71 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.

Solve by factoring and using the principle of zero products. - 12b2+28b+12=−312 b^{2}+28 b+12=-312b2+28b+12=−3

Factor. - 3x4−18x3+24x23 x^{4}-18 x^{3}+24 x^{2}3x4−18x3+24x2

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

Factor. - 45x2+60xy+20y245 x^{2}+60 x y+20 y^{2}45x2+60xy+20y2

Determine whether the following is a difference of squares. - −9x2+9y2-9 x^{2}+9 y^{2}−9x2+9y2

Factor completely. - 64x−25x364 \mathrm{x}-25 \mathrm{x}^{3}64x−25x3

Factor using the ac-method. - −30x2−25x+30-30 x^{2}-25 x+30−30x2−25x+30

Factor. - x3−x2−30xx^{3}-x^{2}-30 xx3−x2−30x

Find the GCF. - x7y7,x6y5,x6y6,−x2y2x^{7} y^{7}, x^{6} y^{5}, x^{6} y^{6},-x^{2} y^{2}x7y7,x6y5,x6y6,−x2y2

Solve by factoring and using the principle of zero products. - 5x2−40x+75=05 x^{2}-40 x+75=05x2−40x+75=0

Solve using the principle of zero products. - (x−3)(x+74)(2x+14)=0(x-3)(x+74)(2 x+14)=0(x−3)(x+74)(2x+14)=0

Solve the problem. -If an object is dropped, the distance it falls is given by d=16t2d=16 t^{2}d=16t2 . Find the distance an object would fall in 6 seconds.

Factor completely. - −36x3−33x2+45x-36 x^{3}-33 x^{2}+45 x−36x3−33x2+45x

Factor completely. - x4−81x^{4}-81x4−81

Factor completely. - 6x2(p+q2)−(p+q2)6 x^{2}\left(p+q^{2}\right)-\left(p+q^{2}\right)6x2(p+q2)−(p+q2)

Solve by factoring and using the principle of zero products. - 28n2+56n=028 n^{2}+56 n=028n2+56n=0

Determine whether the following is a difference of squares. - x2−49x^{2}-49x2−49

Factor completely. - 9x2+18x+89 x^{2}+18 x+89x2+18x+8