Question 1

Divide. Assume all variables are nonzero
-$\frac{16 x^{8}}{-4 x^{3}}$

Accepted Answer

A)  $4 x^{11}$ 
B)  $-4 x^{5}$ 
C)  $4 x^{5}$ 
D)  $-4 x^{11}$ 
A)  $4 x^{11}$ 
B)  $-4 x^{5}$ 
C)  $4 x^{5}$ 
D)  $-4 x^{11}$

Question 2

Choose the one alternative that best completes the statement or answers thequestion.
-$(x-6)^{11} \cdot(x-6)^{3}$

Accepted Answer

A)  $(2 x-12 x+36)^{33}$ 
B)  $(x-6)^{14}$ 
C)  $(x-6)^{33}$ 
D)  $(2 x-12)^{14}$ 
A)  $(2 x-12 x+36)^{33}$ 
B)  $(x-6)^{14}$ 
C)  $(x-6)^{33}$ 
D)  $(2 x-12)^{14}$

Question 3

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}+23 x-24$

Accepted Answer

A)  $(x+24)(x-1)$ 
B)  $(x-6)(x+4)$ 
C)  $(x+6)(x-4)$ 
D)  Prime 
A)  $(x+24)(x-1)$ 
B)  $(x-6)(x+4)$ 
C)  $(x+6)(x-4)$ 
D)  Prime

Question 4

Find the special product using the appropriate formula
-$(8 x+11)^{2}$

Accepted Answer

A)  $8 x^{2}+176 x+121$ 
B)  $64 x^{2}+176 x+121$ 
C)  $8 x^{2}+121$ 
D)  $64 x^{2}+121$ 
A)  $8 x^{2}+176 x+121$ 
B)  $64 x^{2}+176 x+121$ 
C)  $8 x^{2}+121$ 
D)  $64 x^{2}+121$

Question 5

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\left(\frac{x}{3 y}\right)^{-4}$

Accepted Answer

A)  $\frac{x^{4}}{81 y^{4}}$ 
B)  $\frac{3 y^{4}}{x^{4}}$ 
C)  $-\frac{x^{4}}{81 y^{4}}$ 
D)  $\frac{81 y^{4}}{x^{4}}$ 
A)  $\frac{x^{4}}{81 y^{4}}$ 
B)  $\frac{3 y^{4}}{x^{4}}$ 
C)  $-\frac{x^{4}}{81 y^{4}}$ 
D)  $\frac{81 y^{4}}{x^{4}}$

Question 6

Divide. Assume all variables are nonzero
-$\frac{40 x^{4}-35 x^{3}-40 x^{2}-35 x}{5 x}$

Accepted Answer

A)  $8 x^{3}+7 x^{2}-8 x-7$ 
B)  $8 x^{3}-7 x^{2}+8 x-7$ 
C)  $8 x^{3}-7 x^{2}-8 x+7$ 
D)  $8 x^{3}-7 x^{2}-8 x-7$ 
A)  $8 x^{3}+7 x^{2}-8 x-7$ 
B)  $8 x^{3}-7 x^{2}+8 x-7$ 
C)  $8 x^{3}-7 x^{2}-8 x+7$ 
D)  $8 x^{3}-7 x^{2}-8 x-7$

Question 7

In a state with a population of $7,000,000$ people, the average citizen spends $\$ 6,000$ on housing each year. What is the total spent on housing for the state?

Accepted Answer

A)  $\$ 42 \times 10^{11}$ 
B)  $\$ 42 \times 10^{10}$ 
C)  $\$ 4.2 \times 10^{10}$ 
D)  $\$ 4.2 \times 10^{9}$ 
A)  $\$ 42 \times 10^{11}$ 
B)  $\$ 42 \times 10^{10}$ 
C)  $\$ 4.2 \times 10^{10}$ 
D)  $\$ 4.2 \times 10^{9}$

Question 8

Perform the indicated calculation. Express your answer using scientific notation.
-$(0.0000000055)(190,000,000,000)$

Accepted Answer

A)  $1.05 \times 10^{-3}$ 
B)  $1.05 \times 10^{4}$ 
C)  $1.05 \times 10^{3}$ 
D)  $1.05 \times 10^{2}$ 
A)  $1.05 \times 10^{-3}$ 
B)  $1.05 \times 10^{4}$ 
C)  $1.05 \times 10^{3}$ 
D)  $1.05 \times 10^{2}$

Question 9

$(x+4)\left(x^{2}-x+8\right)$

Accepted Answer

A)  $x^{3}+32$ 
B)  $x^{3}+5 x^{2}+12 x+32$ 
C)  $x^{3}+3 x^{2}+32$ 
D)  $x^{3}+3 x^{2}+4 x+32$ 
A)  $x^{3}+32$ 
B)  $x^{3}+5 x^{2}+12 x+32$ 
C)  $x^{3}+3 x^{2}+32$ 
D)  $x^{3}+3 x^{2}+4 x+32$

Question 10

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$3^{-2}$

Accepted Answer

A)  -9 
B)  $\frac{1}{9}$ 
C)  $\frac{1}{6}$ 
D)  9 
A)  -9 
B)  $\frac{1}{9}$ 
C)  $\frac{1}{6}$ 
D)  9

Question 11

Find the GCF.
-$4 x^{2} y^{8}, 16 y^{2} z^{4}$

Accepted Answer

A)  $4 y^{2}$ 
B)  $4 x y z$ 
C)  $x^{2} y^{2}$ 
D)  $2 y^{2}$ 
A)  $4 y^{2}$ 
B)  $4 x y z$ 
C)  $x^{2} y^{2}$ 
D)  $2 y^{2}$

Question 12

Simplify. (A ssume all variables are nonzero.)
-$\left(\frac{a^{3} b^{6}}{b^{2} c^{3}}\right)^{6}$

Accepted Answer

A)  $\frac{a^{18}}{c^{18}}$ 
B)  0 
C)  $\frac{a^{18} b^{24}}{c^{18}}$ 
D)  $\frac{\mathrm{a}^{9} \mathrm{~b}^{24}}{\mathrm{c}^{9}}$ 
A)  $\frac{a^{18}}{c^{18}}$ 
B)  0 
C)  $\frac{a^{18} b^{24}}{c^{18}}$ 
D)  $\frac{\mathrm{a}^{9} \mathrm{~b}^{24}}{\mathrm{c}^{9}}$

Question 13

Find the GCF.
-50, 37

Accepted Answer

A)  37 
B)  5 
C)  1 
D)  10 
A)  37 
B)  5 
C)  1 
D)  10

Question 14

Find the special product using the appropriate formula
-$f(x)=x+7, g(x)=x-10$

Accepted Answer

A)  $x^{2}-3 x-70$ 
B)  $x^{2}+70$ 
C)  $x^{2}+3 x-70$ 
D)  $x^{2}+17 x+70$ 
A)  $x^{2}-3 x-70$ 
B)  $x^{2}+70$ 
C)  $x^{2}+3 x-70$ 
D)  $x^{2}+17 x+70$

Question 15

Factor completely. If the polynomial cannot be factored, write "prime."
-$-x^{2}-5 x+14$

Accepted Answer

A)  $(x+2)(x-7)$ 
B)  $-(x-2)(x+7)$ 
C)  $-(x-2)(x-7)$ 
D)  Prime 
A)  $(x+2)(x-7)$ 
B)  $-(x-2)(x+7)$ 
C)  $-(x-2)(x-7)$ 
D)  Prime

Question 16

List the degree of each term and the degree of the polynomial.
-$4 x^{7} y^{7}-4 x^{2} y^{2}+5 x^{4} y$

Accepted Answer

A)  7,2,5; polynomial: 7 
B)  14, 4, 5; polynomial: 5 
C)  49, 4, 5; polynomial: 49 
D)  14, 4, 5; polynomial: 14 
A)  7,2,5; polynomial: 7 
B)  14, 4, 5; polynomial: 5 
C)  49, 4, 5; polynomial: 49 
D)  14, 4, 5; polynomial: 14

Question 17

Factor completely. If the polynomial cannot be factored, write "prime."
-$4 y^{4}-49$

Accepted Answer

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

Question 18

Simplify. (A ssume all variables are nonzero.)
-$\left(16 x^{6} y^{8} z^{5}\right)^{0}$

Accepted Answer

A)  0 
B)  $16 x ^{6} y^{8} z^{5}$ 
C)  1 
D)  16 
A)  0 
B)  $16 x ^{6} y^{8} z^{5}$ 
C)  1 
D)  16

Question 19

Convert the given number to scientific notation
-0.00000097102

Accepted Answer

A)  $9.7102 \times 10^{-7}$ 
B)  $9.7102 \times 10^{6}$ 
C)  $9.7102 \times 10^{7}$ 
D)  $9.7102 \times 10^{-6}$ 
A)  $9.7102 \times 10^{-7}$ 
B)  $9.7102 \times 10^{6}$ 
C)  $9.7102 \times 10^{7}$ 
D)  $9.7102 \times 10^{-6}$

Question 20

$\left(6 x^{2}-3 x+20\right)-\left(4 x^{2}+6 x-40\right)$

Accepted Answer

A)  $2 x^{2}--9 x+60$ 
B)  $2 x^{2}-9 x-20$ 
C)  $2 x^{2}-9 x+60$ 
D)  $2 x^{2}+9 x+60$ 
A)  $2 x^{2}--9 x+60$ 
B)  $2 x^{2}-9 x-20$ 
C)  $2 x^{2}-9 x+60$ 
D)  $2 x^{2}+9 x+60$

Divide. Assume all variables are nonzero - $\frac{16 x^{8}}{-4 x^{3}}$

Choose the one alternative that best completes the statement or answers thequestion. - $(x-6)^{11} \cdot(x-6)^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+23 x-24$

Find the special product using the appropriate formula - $(8 x+11)^{2}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(\frac{x}{3 y}\right)^{-4}$

Divide. Assume all variables are nonzero - $\frac{40 x^{4}-35 x^{3}-40 x^{2}-35 x}{5 x}$

In a state with a population of $7,000,000$ people, the average citizen spends $\$ 6,000$ on housing each year. What is the total spent on housing for the state?

Perform the indicated calculation. Express your answer using scientific notation. - $(0.0000000055)(190,000,000,000)$

$(x+4)\left(x^{2}-x+8\right)$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $3^{-2}$

Find the GCF. - $4 x^{2} y^{8}, 16 y^{2} z^{4}$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{a^{3} b^{6}}{b^{2} c^{3}}\right)^{6}$

Find the GCF. -50, 37

Find the special product using the appropriate formula - $f(x)=x+7, g(x)=x-10$

Factor completely. If the polynomial cannot be factored, write "prime." - $-x^{2}-5 x+14$

List the degree of each term and the degree of the polynomial. - $4 x^{7} y^{7}-4 x^{2} y^{2}+5 x^{4} y$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 y^{4}-49$

Simplify. (A ssume all variables are nonzero.) - $\left(16 x^{6} y^{8} z^{5}\right)^{0}$

Convert the given number to scientific notation -0.00000097102

$\left(6 x^{2}-3 x+20\right)-\left(4 x^{2}+6 x-40\right)$

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents, Polynomials, and Factoring Polynomials

Divide. Assume all variables are nonzero - 16x8−4x3\frac{16 x^{8}}{-4 x^{3}}−4x316x8​

Choose the one alternative that best completes the statement or answers thequestion. - (x−6)11⋅(x−6)3(x-6)^{11} \cdot(x-6)^{3}(x−6)11⋅(x−6)3

Factor completely. If the polynomial cannot be factored, write "prime." - x2+23x−24x^{2}+23 x-24x2+23x−24

Find the special product using the appropriate formula - (8x+11)2(8 x+11)^{2}(8x+11)2

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - (x3y)−4\left(\frac{x}{3 y}\right)^{-4}(3yx​)−4

Divide. Assume all variables are nonzero - 40x4−35x3−40x2−35x5x\frac{40 x^{4}-35 x^{3}-40 x^{2}-35 x}{5 x}5x40x4−35x3−40x2−35x​

In a state with a population of 7,000,0007,000,0007,000,000 people, the average citizen spends $6,000\$ 6,000$6,000 on housing each year. What is the total spent on housing for the state?

Perform the indicated calculation. Express your answer using scientific notation. - (0.0000000055)(190,000,000,000)(0.0000000055)(190,000,000,000)(0.0000000055)(190,000,000,000)

(x+4)(x2−x+8)(x+4)\left(x^{2}-x+8\right)(x+4)(x2−x+8)

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - 3−23^{-2}3−2

Find the GCF. - 4x2y8,16y2z44 x^{2} y^{8}, 16 y^{2} z^{4}4x2y8,16y2z4

Simplify. (A ssume all variables are nonzero.) - (a3b6b2c3)6\left(\frac{a^{3} b^{6}}{b^{2} c^{3}}\right)^{6}(b2c3a3b6​)6

Find the GCF. -50, 37

Find the special product using the appropriate formula - f(x)=x+7,g(x)=x−10f(x)=x+7, g(x)=x-10f(x)=x+7,g(x)=x−10

Factor completely. If the polynomial cannot be factored, write "prime." - −x2−5x+14-x^{2}-5 x+14−x2−5x+14

List the degree of each term and the degree of the polynomial. - 4x7y7−4x2y2+5x4y4 x^{7} y^{7}-4 x^{2} y^{2}+5 x^{4} y4x7y7−4x2y2+5x4y

Factor completely. If the polynomial cannot be factored, write "prime." - 4y4−494 y^{4}-494y4−49

Simplify. (A ssume all variables are nonzero.) - (16x6y8z5)0\left(16 x^{6} y^{8} z^{5}\right)^{0}(16x6y8z5)0

Convert the given number to scientific notation -0.00000097102

(6x2−3x+20)−(4x2+6x−40)\left(6 x^{2}-3 x+20\right)-\left(4 x^{2}+6 x-40\right)(6x2−3x+20)−(4x2+6x−40)

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Rational Expressions and Equations

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Divide. Assume all variables are nonzero - $\frac{16 x^{8}}{-4 x^{3}}$

Choose the one alternative that best completes the statement or answers thequestion. - $(x-6)^{11} \cdot(x-6)^{3}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+23 x-24$

Find the special product using the appropriate formula - $(8 x+11)^{2}$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\left(\frac{x}{3 y}\right)^{-4}$

Divide. Assume all variables are nonzero - $\frac{40 x^{4}-35 x^{3}-40 x^{2}-35 x}{5 x}$

In a state with a population of $7,000,000$ people, the average citizen spends $\$ 6,000$ on housing each year. What is the total spent on housing for the state?

Perform the indicated calculation. Express your answer using scientific notation. - $(0.0000000055)(190,000,000,000)$

$(x+4)\left(x^{2}-x+8\right)$

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $3^{-2}$

Find the GCF. - $4 x^{2} y^{8}, 16 y^{2} z^{4}$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{a^{3} b^{6}}{b^{2} c^{3}}\right)^{6}$

Find the special product using the appropriate formula - $f(x)=x+7, g(x)=x-10$

Factor completely. If the polynomial cannot be factored, write "prime." - $-x^{2}-5 x+14$

List the degree of each term and the degree of the polynomial. - $4 x^{7} y^{7}-4 x^{2} y^{2}+5 x^{4} y$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 y^{4}-49$

Simplify. (A ssume all variables are nonzero.) - $\left(16 x^{6} y^{8} z^{5}\right)^{0}$

$\left(6 x^{2}-3 x+20\right)-\left(4 x^{2}+6 x-40\right)$