Question 1

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.)
-$\frac{1}{\mathrm{x}^{-4}}$

Accepted Answer

A)  $\frac{1}{x^{4}}$ 
B)  $x^{4}$ 
C)  $x^{-4}$ 
D)  $4 x$ 
A)  $\frac{1}{x^{4}}$ 
B)  $x^{4}$ 
C)  $x^{-4}$ 
D)  $4 x$

Question 2

Find the GCF.
-$54,72,126$

Accepted Answer

A)  9 
B)  36 
C)  2 
D)  18 
A)  9 
B)  36 
C)  2 
D)  18

Question 3

$-6 x^{5} \cdot 8 x^{8} \cdot 3 x^{6}$

Accepted Answer

A)  $144 x^{19}$ 
B)  $144 x^{240}$ 
C)  $-144 x^{19}$ 
D)  $-144 x^{240}$ 
A)  $144 x^{19}$ 
B)  $144 x^{240}$ 
C)  $-144 x^{19}$ 
D)  $-144 x^{240}$

Question 4

Identify the polynomial as a 
-$12 x^{4}-2 x^{3}+2 x^{2}$

Accepted Answer

A)  Monomial 
B)  Trinomial 
C)  Binomial 
A)  Monomial 
B)  Trinomial 
C)  Binomial

Question 5

Convert the given number to standard notation
-$6.939 \times 10^{-6}$

Accepted Answer

A)  0.000006939 
B)  0.00006939 
C)  $-6,939,000$ 
D)  0.0000006939 
A)  0.000006939 
B)  0.00006939 
C)  $-6,939,000$ 
D)  0.0000006939

Question 6

Simplify. (A ssume all variables are nonzero.)
-$\left(\frac{3}{4}\right)^{2}$

Accepted Answer

A)  $2 \frac{3}{4}$ 
B)  $\frac{9}{16}$ 
C)  $\frac{16}{9}$ 
D)  $\frac{9}{4}$ 
A)  $2 \frac{3}{4}$ 
B)  $\frac{9}{16}$ 
C)  $\frac{16}{9}$ 
D)  $\frac{9}{4}$

Question 7

$36 x^{2}+24 x=0$

Accepted Answer

A)  $\{0\}$ 
B)  $\left\{-\frac{2}{3}, 0\right\}$ 
C)  $\left\{-\frac{2}{3}, 24\right\}$ 
D)  $\left\{-\frac{2}{3}\right\}$ 
A)  $\{0\}$ 
B)  $\left\{-\frac{2}{3}, 0\right\}$ 
C)  $\left\{-\frac{2}{3}, 24\right\}$ 
D)  $\left\{-\frac{2}{3}\right\}$

Question 8

Simplify. (A ssume all variables are nonzero.)
-$\mathrm{z}^{35} \div \mathrm{z}^{5}$

Accepted Answer

A)  $z^{7}$ 
B)  $z^{30}$ 
C)  $z^{40}$ 
D)  $z^{175}$ 
A)  $z^{7}$ 
B)  $z^{30}$ 
C)  $z^{40}$ 
D)  $z^{175}$

Question 9

Evaluate the polynomial or polynomial function for the given value of the variable.
-$f(x)=7 x^{3}+2 x^{2}-3 x+2, f(-2)$

Accepted Answer

A)  60 
B)  -49 
C)  -68 
D)  -40 
A)  60 
B)  -49 
C)  -68 
D)  -40

Question 10

Convert the given number to standard notation
-$3.38 \times 10^{4}$

Accepted Answer

A)  338,000 
B)  33,800 
C)  3380 
D)  135.2 
A)  338,000 
B)  33,800 
C)  3380 
D)  135.2

Question 11

Factor the GCF out of the given expression.
-$28 x^{9} y^{7}-8 x^{5} y^{4}+12 x^{2} y^{2}$

Accepted Answer

A)  $4\left(7 x^{9} y^{7}-2 x^{5} y^{4}+3 x^{2} y^{2}\right)$ 
B)  $x^{2}\left(7 x^{7} y^{7}-2 x^{3} y^{4}+3 y^{2}\right)$ 
C)  $4 x^{2} y^{2}\left(7 x^{7} y^{5}-2 x^{3} y^{2}+3\right)$ 
D)  $4 x^{2}\left(7 x^{7} y^{7}-2 x^{3} y^{4}+3 y^{2}\right)$ 
A)  $4\left(7 x^{9} y^{7}-2 x^{5} y^{4}+3 x^{2} y^{2}\right)$ 
B)  $x^{2}\left(7 x^{7} y^{7}-2 x^{3} y^{4}+3 y^{2}\right)$ 
C)  $4 x^{2} y^{2}\left(7 x^{7} y^{5}-2 x^{3} y^{2}+3\right)$ 
D)  $4 x^{2}\left(7 x^{7} y^{7}-2 x^{3} y^{4}+3 y^{2}\right)$

Question 12

Simplify. (A ssume all variables are nonzero.)
-$\frac{x^{7}}{x^{4}}$

Accepted Answer

A)  $x^{1.8}$ 
B)  $x^{3}$ 
C)  $x^{11}$ 
D)  1.8 
A)  $x^{1.8}$ 
B)  $x^{3}$ 
C)  $x^{11}$ 
D)  1.8

Question 13

$\frac{2}{3} x^{2}-\frac{17}{6} x-\frac{5}{2}=0$

Accepted Answer

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

Question 14

Determine whether the simplified version of the given expression would be a
-$(4 \mathrm{x}+3)^{2}$

Accepted Answer

A)  trinomial 
B)  polynomial with four or more terms 
C)  binomial 
A)  trinomial 
B)  polynomial with four or more terms 
C)  binomial

Question 15

Evaluate the polynomial or polynomial function for the given value of the variable.
-$g(x)=-2 x^{2}+6 x-4, g(3)$

Accepted Answer

A)  8 
B)  -4 
C)  -8 
D)  - 14 
A)  8 
B)  -4 
C)  -8 
D)  - 14

Question 16

Choose the one alternative that best completes the statement or answers thequestion.
-$\left(6 x^{4}\right)^{6}$

Accepted Answer

A)  $36 x^{24}$ 
B)  $36 x^{10}$ 
C)  $46,656 x^{24}$ 
D)  $6 x^{24}$ 
A)  $36 x^{24}$ 
B)  $36 x^{10}$ 
C)  $46,656 x^{24}$ 
D)  $6 x^{24}$

Question 17

Factor completely. If the polynomial cannot be factored, write "prime."
-$14 \mathrm{x}^{2}+63 \mathrm{x}-35$

Accepted Answer

A)  $(14 x-7)(x+5)$ 
B)  $(2 x-1)(7 x+35)$ 
C)  $7(2 x+1)(x-5)$ 
D)  $7(2 x-1)(x+5)$ 
A)  $(14 x-7)(x+5)$ 
B)  $(2 x-1)(7 x+35)$ 
C)  $7(2 x+1)(x-5)$ 
D)  $7(2 x-1)(x+5)$

Question 18

Find a quadratic equation with integer coefficients that has the given solution set.
-$\left\{-4, \frac{9}{4}\right\}$

Accepted Answer

A)  $4 x^{2}+7 x-36=0$ 
B)  $4 x^{2}+11 x+36=0$ 
C)  $4 x^{2}-7 x-36=0$ 
D)  $x^{2}-7 x-36=0$ 
A)  $4 x^{2}+7 x-36=0$ 
B)  $4 x^{2}+11 x+36=0$ 
C)  $4 x^{2}-7 x-36=0$ 
D)  $x^{2}-7 x-36=0$

Question 19

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-4$

Accepted Answer

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

Question 20

Find the number of molecules in the given quantity of a compound whose molar mass is given. Express your answer in scientific notation, rounding the decimal part to the nearest hundredth.
-22 grams of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$; molar mass 160.18 grams

Accepted Answer

A)  $8.27 \times 10^{22}$ molecules 
B)  $2.12 \times 10^{27}$ molecules 
C)  $2.12 \times 10^{28}$ molecules 
D)  $8.27 \times 10^{21}$ molecules 
A)  $8.27 \times 10^{22}$ molecules 
B)  $2.12 \times 10^{27}$ molecules 
C)  $2.12 \times 10^{28}$ molecules 
D)  $8.27 \times 10^{21}$ molecules

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{1}{\mathrm{x}^{-4}}$

Find the GCF. - $54,72,126$

$-6 x^{5} \cdot 8 x^{8} \cdot 3 x^{6}$

Identify the polynomial as a - $12 x^{4}-2 x^{3}+2 x^{2}$

Convert the given number to standard notation - $6.939 \times 10^{-6}$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{3}{4}\right)^{2}$

$36 x^{2}+24 x=0$

Simplify. (A ssume all variables are nonzero.) - $\mathrm{z}^{35} \div \mathrm{z}^{5}$

Evaluate the polynomial or polynomial function for the given value of the variable. - $f(x)=7 x^{3}+2 x^{2}-3 x+2, f(-2)$

Convert the given number to standard notation - $3.38 \times 10^{4}$

Factor the GCF out of the given expression. - $28 x^{9} y^{7}-8 x^{5} y^{4}+12 x^{2} y^{2}$

Simplify. (A ssume all variables are nonzero.) - $\frac{x^{7}}{x^{4}}$

$\frac{2}{3} x^{2}-\frac{17}{6} x-\frac{5}{2}=0$

Determine whether the simplified version of the given expression would be a - $(4 \mathrm{x}+3)^{2}$

Evaluate the polynomial or polynomial function for the given value of the variable. - $g(x)=-2 x^{2}+6 x-4, g(3)$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(6 x^{4}\right)^{6}$

Factor completely. If the polynomial cannot be factored, write "prime." - $14 \mathrm{x}^{2}+63 \mathrm{x}-35$

Find a quadratic equation with integer coefficients that has the given solution set. - $\left\{-4, \frac{9}{4}\right\}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-4$

Find the number of molecules in the given quantity of a compound whose molar mass is given. Express your answer in scientific notation, rounding the decimal part to the nearest hundredth. -22 grams of glucose $\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)$ ; molar mass 160.18 grams

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

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - 1x−4\frac{1}{\mathrm{x}^{-4}}x−41​

Find the GCF. - 54,72,12654,72,12654,72,126

−6x5⋅8x8⋅3x6-6 x^{5} \cdot 8 x^{8} \cdot 3 x^{6}−6x5⋅8x8⋅3x6

Identify the polynomial as a - 12x4−2x3+2x212 x^{4}-2 x^{3}+2 x^{2}12x4−2x3+2x2

Convert the given number to standard notation - 6.939×10−66.939 \times 10^{-6}6.939×10−6

Simplify. (A ssume all variables are nonzero.) - (34)2\left(\frac{3}{4}\right)^{2}(43​)2

36x2+24x=036 x^{2}+24 x=036x2+24x=0

Simplify. (A ssume all variables are nonzero.) - z35÷z5\mathrm{z}^{35} \div \mathrm{z}^{5}z35÷z5

Evaluate the polynomial or polynomial function for the given value of the variable. - f(x)=7x3+2x2−3x+2,f(−2)f(x)=7 x^{3}+2 x^{2}-3 x+2, f(-2)f(x)=7x3+2x2−3x+2,f(−2)

Convert the given number to standard notation - 3.38×1043.38 \times 10^{4}3.38×104

Factor the GCF out of the given expression. - 28x9y7−8x5y4+12x2y228 x^{9} y^{7}-8 x^{5} y^{4}+12 x^{2} y^{2}28x9y7−8x5y4+12x2y2

Simplify. (A ssume all variables are nonzero.) - x7x4\frac{x^{7}}{x^{4}}x4x7​

23x2−176x−52=0\frac{2}{3} x^{2}-\frac{17}{6} x-\frac{5}{2}=032​x2−617​x−25​=0

Determine whether the simplified version of the given expression would be a - (4x+3)2(4 \mathrm{x}+3)^{2}(4x+3)2

Evaluate the polynomial or polynomial function for the given value of the variable. - g(x)=−2x2+6x−4,g(3)g(x)=-2 x^{2}+6 x-4, g(3)g(x)=−2x2+6x−4,g(3)

Choose the one alternative that best completes the statement or answers thequestion. - (6x4)6\left(6 x^{4}\right)^{6}(6x4)6

Factor completely. If the polynomial cannot be factored, write "prime." - 14x2+63x−3514 \mathrm{x}^{2}+63 \mathrm{x}-3514x2+63x−35

Find a quadratic equation with integer coefficients that has the given solution set. - {−4,94}\left\{-4, \frac{9}{4}\right\}{−4,49​}

Factor completely. If the polynomial cannot be factored, write "prime." - x2−4x^{2}-4x2−4

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

Rewrite the expression without using negative exponents. (A ssume all variables represent nonzero real numbers.) - $\frac{1}{\mathrm{x}^{-4}}$

Find the GCF. - $54,72,126$

$-6 x^{5} \cdot 8 x^{8} \cdot 3 x^{6}$

Identify the polynomial as a - $12 x^{4}-2 x^{3}+2 x^{2}$

Convert the given number to standard notation - $6.939 \times 10^{-6}$

Simplify. (A ssume all variables are nonzero.) - $\left(\frac{3}{4}\right)^{2}$

$36 x^{2}+24 x=0$

Simplify. (A ssume all variables are nonzero.) - $\mathrm{z}^{35} \div \mathrm{z}^{5}$

Evaluate the polynomial or polynomial function for the given value of the variable. - $f(x)=7 x^{3}+2 x^{2}-3 x+2, f(-2)$

Convert the given number to standard notation - $3.38 \times 10^{4}$

Factor the GCF out of the given expression. - $28 x^{9} y^{7}-8 x^{5} y^{4}+12 x^{2} y^{2}$

Simplify. (A ssume all variables are nonzero.) - $\frac{x^{7}}{x^{4}}$

$\frac{2}{3} x^{2}-\frac{17}{6} x-\frac{5}{2}=0$

Determine whether the simplified version of the given expression would be a - $(4 \mathrm{x}+3)^{2}$

Evaluate the polynomial or polynomial function for the given value of the variable. - $g(x)=-2 x^{2}+6 x-4, g(3)$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(6 x^{4}\right)^{6}$

Factor completely. If the polynomial cannot be factored, write "prime." - $14 \mathrm{x}^{2}+63 \mathrm{x}-35$

Find a quadratic equation with integer coefficients that has the given solution set. - $\left\{-4, \frac{9}{4}\right\}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-4$