Question 1

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

Accepted Answer

A)  $\frac{a^{6}}{b^{6}}$ 
B)  $\frac{6 a}{6 b}$ 
C)  6 
D)  $\frac{a^{6}}{b}$ 
A)  $\frac{a^{6}}{b^{6}}$ 
B)  $\frac{6 a}{6 b}$ 
C)  6 
D)  $\frac{a^{6}}{b}$

Question 2

Factor completely. If the polynomial cannot be factored, write "prime."
-$8 x^{2}+6 x-9$

Accepted Answer

A)  $(8 x-3)(x-9)$ 
B)  $(4 x-3)(2 x+3)$ 
C)  $(8 x-3)(x+3)$ 
D)  $(4 x+3)(2 x-3)$ 
A)  $(8 x-3)(x-9)$ 
B)  $(4 x-3)(2 x+3)$ 
C)  $(8 x-3)(x+3)$ 
D)  $(4 x+3)(2 x-3)$

Question 3

Factor completely. If the polynomial cannot be factored, write "prime."
-$343-729 x^{3}$

Accepted Answer

A)  $(7-9 x)\left(49+81 x^{2}\right)$ 
B)  $(343-9 x)\left(1+63 x+81 x^{2}\right)$ 
C)  $(7+9 x)\left(49-63 x+81 x^{2}\right)$ 
D)  $(7-9 x)\left(49+63 x+81 x^{2}\right)$ 
A)  $(7-9 x)\left(49+81 x^{2}\right)$ 
B)  $(343-9 x)\left(1+63 x+81 x^{2}\right)$ 
C)  $(7+9 x)\left(49-63 x+81 x^{2}\right)$ 
D)  $(7-9 x)\left(49+63 x+81 x^{2}\right)$

Question 4

Round your answer to the nearest whole number, if necessary.
-Cindy determines that the revenue generated by candy sales for her high school can be approximated by the function $\mathrm{R}(\mathrm{x})=9 \mathrm{x}+2$, where $\mathrm{x}$ represents the price of the candy in dollars. How much money will be generated if the candy is sold for $\$ 6$ ?

Accepted Answer

A)  $\$ 52$ 
B)  $\$ 108$ 
C)  $\$ 11$ 
D)  $\$ 56$ 
A)  $\$ 52$ 
B)  $\$ 108$ 
C)  $\$ 11$ 
D)  $\$ 56$

Question 5

Identify the polynomial as a 
-$14 x^{5}-8 x^{4}-4$

Accepted Answer

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

Question 6

For the given functions $f(x)$ and $g(x)$, perform the indicated operation.
-$f(x)=x^{3}-9 x-23, g(x)=4 x^{3}+x^{2}+7 x+10$
Find $f(x)+g(x)$.

Accepted Answer

A)  $4 x^{3}+x^{2}-2 x-13$ 
B)  $5 x^{3}+x^{2}-2 x-13$ 
C)  $5 x^{3}+x^{2}-16 x-33$ 
D)  $5 x^{3}-x^{2}-2 x+13$ 
A)  $4 x^{3}+x^{2}-2 x-13$ 
B)  $5 x^{3}+x^{2}-2 x-13$ 
C)  $5 x^{3}+x^{2}-16 x-33$ 
D)  $5 x^{3}-x^{2}-2 x+13$

Question 7

Divide using long division.
-$\frac{-12 x^{3}-27 x^{2}-35 x-11}{-4 x-5}$

Accepted Answer

A)  $3 x^{2}+3 x+5$ 
B)  $3 x^{2}+3 x+5+\frac{17}{-4 x-5}$ 
C)  $x^{2}+5+\frac{3}{-4 x-5}$ 
D)  $3 x^{2}+3 x+5+\frac{14}{-4 x-5}$ 
A)  $3 x^{2}+3 x+5$ 
B)  $3 x^{2}+3 x+5+\frac{17}{-4 x-5}$ 
C)  $x^{2}+5+\frac{3}{-4 x-5}$ 
D)  $3 x^{2}+3 x+5+\frac{14}{-4 x-5}$

Question 8

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

Accepted Answer

A)  $\frac{8 a^{9} b^{9}}{c^{12}}$ 
B)  $\frac{2 a^{9} b^{9}}{c^{12}}$ 
C)  $\frac{2 \mathrm{a}^{9} \mathrm{~b}^{9}}{\mathrm{c}^{7}}$ 
D)  $\frac{8 a^{6} b^{6}}{c^{7}}$ 
A)  $\frac{8 a^{9} b^{9}}{c^{12}}$ 
B)  $\frac{2 a^{9} b^{9}}{c^{12}}$ 
C)  $\frac{2 \mathrm{a}^{9} \mathrm{~b}^{9}}{\mathrm{c}^{7}}$ 
D)  $\frac{8 a^{6} b^{6}}{c^{7}}$

Question 9

Choose the one alternative that best completes the statement or answers thequestion.
-$\left(a^{4}\right)^{8}$

Accepted Answer

A)  $a^{32}$ 
B)  $a^{8}$ 
C)  $a^{14}$ 
D)  $a^{12}$ 
A)  $a^{32}$ 
B)  $a^{8}$ 
C)  $a^{14}$ 
D)  $a^{12}$

Question 10

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-4 x-77$

Accepted Answer

A)  $(x-7)(x+11)$ 
B)  $(x-7)(x+1)$ 
C)  $(x+7)(x-11)$ 
D)  Prime 
A)  $(x-7)(x+11)$ 
B)  $(x-7)(x+1)$ 
C)  $(x+7)(x-11)$ 
D)  Prime

Question 11

Factor completely. If the polynomial cannot be factored, write "prime."
-$49 x^{5}-100 x$

Accepted Answer

A)  $\left(7 x^{2}+10\right)\left(7 x^{2}-10\right)$ 
B)  $x\left(7 x^{2}+10\right)(x+1)(x-1)$ 
C)  $x\left(7 x^{2}+10\right)\left(7 x^{2}-10\right)$ 
D)  Prime 
A)  $\left(7 x^{2}+10\right)\left(7 x^{2}-10\right)$ 
B)  $x\left(7 x^{2}+10\right)(x+1)(x-1)$ 
C)  $x\left(7 x^{2}+10\right)\left(7 x^{2}-10\right)$ 
D)  Prime

Question 12

Factor completely. If the polynomial cannot be factored, write "prime."
-$4 x^{2}+81$

Accepted Answer

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

Question 13

Divide. Assume all variables are nonzero
-$\frac{32 x^{3}-48 x}{8}$

Accepted Answer

A)  $4 x^{3}-6 x$ 
B)  $4 x^{3}-48 x$ 
C)  $4 x^{2}-6$ 
D)  $32 x^{3}-6 x$ 
A)  $4 x^{3}-6 x$ 
B)  $4 x^{3}-48 x$ 
C)  $4 x^{2}-6$ 
D)  $32 x^{3}-6 x$

Question 14

Factor the GCF out of the given expression.
-$5 t^{2}-15 t-20$

Accepted Answer

A)  $5\left(t^{2}-15 t-20\right)$ 
B)  $5\left(t^{2}-3 t-4\right)$ 
C)  $5 \mathrm{t}\left(\mathrm{t}^{2}-3 \mathrm{t}-4\right)$ 
D)  $5\left(t^{2}-10 t-15\right)$ 
A)  $5\left(t^{2}-15 t-20\right)$ 
B)  $5\left(t^{2}-3 t-4\right)$ 
C)  $5 \mathrm{t}\left(\mathrm{t}^{2}-3 \mathrm{t}-4\right)$ 
D)  $5\left(t^{2}-10 t-15\right)$

Question 15

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial.
-$3 x^{6}-9 x^{7}+10 x^{2}-8$

Accepted Answer

A)  $3 x^{6}, 3,7$ 
B)  $-9 x^{7},-9,7$ 
C)  $9 x^{7}, 9,7$ 
D)  $3 x^{6}, 3,6$ 
A)  $3 x^{6}, 3,7$ 
B)  $-9 x^{7},-9,7$ 
C)  $9 x^{7}, 9,7$ 
D)  $3 x^{6}, 3,6$

Question 16

Simplify. (A ssume all variables are nonzero.)
-$\frac{8 y^{3}}{4 y}$

Accepted Answer

A)  $4 y^{2}$ 
B)  $2 \mathrm{y}$ 
C)  $2 y^{2}$ 
D)  4 
A)  $4 y^{2}$ 
B)  $2 \mathrm{y}$ 
C)  $2 y^{2}$ 
D)  4

Question 17

Find the special product using the appropriate formula
-$f(x)=12 x^{7}, g(x)=-9 x^{7}-2 x^{6}+11$

Accepted Answer

A)  $-108 x^{14}-2 x^{6}+11$ 
B)  $-108 x^{14}-24 x^{13}$ 
C)  $-108 x^{7}-24 x^{6}+132$ 
D)  $-108 x^{14}-24 x^{13}+132 x^{7}$ 
A)  $-108 x^{14}-2 x^{6}+11$ 
B)  $-108 x^{14}-24 x^{13}$ 
C)  $-108 x^{7}-24 x^{6}+132$ 
D)  $-108 x^{14}-24 x^{13}+132 x^{7}$

Question 18

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}-2 x-15$

Accepted Answer

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

Question 19

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

Accepted Answer

A)  $\frac{2}{x^{3}}$ 
B)  $8 x^{3}$ 
C)  $\frac{8}{x^{3}}$ 
D)  $\frac{8}{x}$ 
A)  $\frac{2}{x^{3}}$ 
B)  $8 x^{3}$ 
C)  $\frac{8}{x^{3}}$ 
D)  $\frac{8}{x}$

Question 20

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$\frac{y^{-11}}{y^{2}}$

Accepted Answer

A)  $\mathrm{y}^{9}$ 
B)  $y^{13}$ 
C)  $\frac{1}{y^{9}}$ 
D)  $\frac{1}{y^{13}}$ 
A)  $\mathrm{y}^{9}$ 
B)  $y^{13}$ 
C)  $\frac{1}{y^{9}}$ 
D)  $\frac{1}{y^{13}}$

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

Factor completely. If the polynomial cannot be factored, write "prime." - $8 x^{2}+6 x-9$

Factor completely. If the polynomial cannot be factored, write "prime." - $343-729 x^{3}$

Identify the polynomial as a - $14 x^{5}-8 x^{4}-4$

For the given functions $f(x)$ and $g(x)$ , perform the indicated operation. - $f(x)=x^{3}-9 x-23, g(x)=4 x^{3}+x^{2}+7 x+10$ Find $f(x)+g(x)$ .

Divide using long division. - $\frac{-12 x^{3}-27 x^{2}-35 x-11}{-4 x-5}$

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

Choose the one alternative that best completes the statement or answers thequestion. - $\left(a^{4}\right)^{8}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-4 x-77$

Factor completely. If the polynomial cannot be factored, write "prime." - $49 x^{5}-100 x$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{2}+81$

Divide. Assume all variables are nonzero - $\frac{32 x^{3}-48 x}{8}$

Factor the GCF out of the given expression. - $5 t^{2}-15 t-20$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $3 x^{6}-9 x^{7}+10 x^{2}-8$

Simplify. (A ssume all variables are nonzero.) - $\frac{8 y^{3}}{4 y}$

Find the special product using the appropriate formula - $f(x)=12 x^{7}, g(x)=-9 x^{7}-2 x^{6}+11$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}-2 x-15$

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

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac{y^{-11}}{y^{2}}$

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

Simplify. (A ssume all variables are nonzero.) - (ab)6\left(\frac{\mathrm{a}}{\mathrm{b}}\right)^{6}(ba​)6

Factor completely. If the polynomial cannot be factored, write "prime." - 8x2+6x−98 x^{2}+6 x-98x2+6x−9

Factor completely. If the polynomial cannot be factored, write "prime." - 343−729x3343-729 x^{3}343−729x3

Identify the polynomial as a - 14x5−8x4−414 x^{5}-8 x^{4}-414x5−8x4−4

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , perform the indicated operation. - f(x)=x3−9x−23,g(x)=4x3+x2+7x+10f(x)=x^{3}-9 x-23, g(x)=4 x^{3}+x^{2}+7 x+10f(x)=x3−9x−23,g(x)=4x3+x2+7x+10 Find f(x)+g(x)f(x)+g(x)f(x)+g(x) .

Divide using long division. - −12x3−27x2−35x−11−4x−5\frac{-12 x^{3}-27 x^{2}-35 x-11}{-4 x-5}−4x−5−12x3−27x2−35x−11​

Simplify. (A ssume all variables are nonzero.) - (2a3 b3c4)3\left(\frac{2 \mathrm{a}^{3} \mathrm{~b}^{3}}{\mathrm{c}^{4}}\right)^{3}(c42a3 b3​)3

Choose the one alternative that best completes the statement or answers thequestion. - (a4)8\left(a^{4}\right)^{8}(a4)8

Factor completely. If the polynomial cannot be factored, write "prime." - x2−4x−77x^{2}-4 x-77x2−4x−77

Factor completely. If the polynomial cannot be factored, write "prime." - 49x5−100x49 x^{5}-100 x49x5−100x

Factor completely. If the polynomial cannot be factored, write "prime." - 4x2+814 x^{2}+814x2+81

Divide. Assume all variables are nonzero - 32x3−48x8\frac{32 x^{3}-48 x}{8}832x3−48x​

Factor the GCF out of the given expression. - 5t2−15t−205 t^{2}-15 t-205t2−15t−20

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - 3x6−9x7+10x2−83 x^{6}-9 x^{7}+10 x^{2}-83x6−9x7+10x2−8

Simplify. (A ssume all variables are nonzero.) - 8y34y\frac{8 y^{3}}{4 y}4y8y3​

Find the special product using the appropriate formula - f(x)=12x7,g(x)=−9x7−2x6+11f(x)=12 x^{7}, g(x)=-9 x^{7}-2 x^{6}+11f(x)=12x7,g(x)=−9x7−2x6+11

Factor completely. If the polynomial cannot be factored, write "prime." - x2−2x−15x^{2}-2 x-15x2−2x−15

Simplify. (A ssume all variables are nonzero.) - (2x)3\left(\frac{2}{x}\right)^{3}(x2​)3

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - y−11y2\frac{y^{-11}}{y^{2}}y2y−11​