Question 1

Factor completely. If the polynomial cannot be factored, write "prime."
-$9 x^{2}+64$

Accepted Answer

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

Question 2

Divide. Assume all variables are nonzero
-$\frac{30 x^{5}-15 x^{2}+50 x}{5 x}$

Accepted Answer

A)  $30 x^{4}-15 x+50$ 
B)  $6 x^{4}-3 x+10$ 
C)  $6 x^{5}-3 x^{2}+10 x$ 
D)  $6 x^{5}-15 x^{2}+50 x$ 
A)  $30 x^{4}-15 x+50$ 
B)  $6 x^{4}-3 x+10$ 
C)  $6 x^{5}-3 x^{2}+10 x$ 
D)  $6 x^{5}-15 x^{2}+50 x$

Question 3

Find the missing factor or exponent(s).
-$\frac{x^{10} y^{2} ?}{x^{?} y^{19}}=x^{4} y^{6}$

Accepted Answer

A)  19,10 
B)  6,25 
C)  10,6 
D)  6, 19 
A)  19,10 
B)  6,25 
C)  10,6 
D)  6, 19

Question 4

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial.
-$-5 x^{4}-14 x^{2}+7 x+6 x^{6}$

Accepted Answer

A)  $-5 a^{4},-5,4$ 
B)  $-6 a^{6},-6,6$ 
C)  $5 a^{4}, 5,4$ 
D)  $6 a^{6}, 6,6$ 
A)  $-5 a^{4},-5,4$ 
B)  $-6 a^{6},-6,6$ 
C)  $5 a^{4}, 5,4$ 
D)  $6 a^{6}, 6,6$

Question 5

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{2}+5 x+4$

Accepted Answer

A)  $(x+1)(x+4)$ 
B)  $(x+4)(x-1)$ 
C)  $(x+4)(x+5)$ 
D)  $(x-1)(x-4)$ 
A)  $(x+1)(x+4)$ 
B)  $(x+4)(x-1)$ 
C)  $(x+4)(x+5)$ 
D)  $(x-1)(x-4)$

Question 6

Factor completely. If the polynomial cannot be factored, write "prime."
-$x^{4} y^{5}-x^{3} y^{7}$

Accepted Answer

A)  $x^{3} y^{5}(x-y)(x+y)$ 
B)  $x^{3} y^{5}\left(x-y^{2}\right)$ 
C)  $x^{4} y^{5}\left(1-x y^{2}\right)$ 
D)  $x^{4} y^{7}\left(x-y^{2}\right)$ 
A)  $x^{3} y^{5}(x-y)(x+y)$ 
B)  $x^{3} y^{5}\left(x-y^{2}\right)$ 
C)  $x^{4} y^{5}\left(1-x y^{2}\right)$ 
D)  $x^{4} y^{7}\left(x-y^{2}\right)$

Question 7

Choose the one alternative that best completes the statement or answers thequestion.
-$\left(7 x^{2}\right)^{2}$

Accepted Answer

A)  $49 x^{8}$ 
B)  $7 x^{2}$ 
C)  $7 x^{4}$ 
D)  $49 x^{4}$ 
A)  $49 x^{8}$ 
B)  $7 x^{2}$ 
C)  $7 x^{4}$ 
D)  $49 x^{4}$

Question 8

Factor completely. If the polynomial cannot be factored, write "prime."
-$4 x^{2}+4 x-24$

Accepted Answer

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

Question 9

Divide. Assume all variables are nonzero
-$\frac{12 x^{8}+6 x^{6}}{3 x^{4}}$

Accepted Answer

A)  $12 x^{8}+2 x^{2}$ 
B)  $6 x^{10}$ 
C)  $4 x^{4}+2 x^{2}$ 
D)  $4 x^{4}+6 x^{6}$ 
A)  $12 x^{8}+2 x^{2}$ 
B)  $6 x^{10}$ 
C)  $4 x^{4}+2 x^{2}$ 
D)  $4 x^{4}+6 x^{6}$

Question 10

Factor by grouping.
-$15 x^{2}-9 x-10 x+6$

Accepted Answer

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

Question 11

Choose the one alternative that best completes the statement or answers thequestion.
-$\left(3 x^{2} y^{3}\right)^{2}$

Accepted Answer

A)  $3 x^{4} y^ 6$ 
B)  $9 x^{4} y^{6}$ 
C)  $9 x ^4 y^{5}$ 
D)  $3 x^{4} y^{5}$ 
A)  $3 x^{4} y^ 6$ 
B)  $9 x^{4} y^{6}$ 
C)  $9 x ^4 y^{5}$ 
D)  $3 x^{4} y^{5}$

Question 12

If the distance from the earth to the sun were $92,900,000$ miles, how long would it take a rocket, traveling at $3.8 \times 10^{3}$ miles per hour, to reach the sun? Round to three decimal places.

Accepted Answer

A)  $2.4 \times 10^{2}$ hours 
B)  2.4 hours 
C)  $2.4 \times 10^{4}$ hours 
D)  $2.4 \times 10^{3}$ hours 
A)  $2.4 \times 10^{2}$ hours 
B)  2.4 hours 
C)  $2.4 \times 10^{4}$ hours 
D)  $2.4 \times 10^{3}$ hours

Question 13

$x(x+13)=0$

Accepted Answer

A)  $\{1,-13\}$ 
B)  $\{1,-13\}$. 
C)  $\{13,0\}$ 
D)  $\{-13,0\}$ 
A)  $\{1,-13\}$ 
B)  $\{1,-13\}$. 
C)  $\{13,0\}$ 
D)  $\{-13,0\}$

Question 14

Divide. Assume all variables are nonzero
-$\frac{10 x^{10}}{5 x^{8}}$

Accepted Answer

A)  $2 x^{18}$ 
B)  $-2 x^{18}$ 
C)  $5 x^{2}$ 
D)  $2 x^{2}$ 
A)  $2 x^{18}$ 
B)  $-2 x^{18}$ 
C)  $5 x^{2}$ 
D)  $2 x^{2}$

Question 15

Evaluate the given function
-$f(x)=x^{3}, f(-5)$

Accepted Answer

A)  $-5 x^{3}$ 
B)  -125 
C)  -15 
D)  $x^{-15}$ 
A)  $-5 x^{3}$ 
B)  -125 
C)  -15 
D)  $x^{-15}$

Question 16

$12 x^{2}+23 x+10=0$

Accepted Answer

A)  $\left\{\frac{4}{5}, \frac{3}{2}\right\}$ 
B)  $\left\{-\frac{4}{5},-\frac{2}{3}\right\}$ 
C)  $\left\{-\frac{5}{4},-\frac{2}{3}\right\}$ 
D)  $\left\{\frac{5}{4}, \frac{2}{3}\right\}$ 
A)  $\left\{\frac{4}{5}, \frac{3}{2}\right\}$ 
B)  $\left\{-\frac{4}{5},-\frac{2}{3}\right\}$ 
C)  $\left\{-\frac{5}{4},-\frac{2}{3}\right\}$ 
D)  $\left\{\frac{5}{4}, \frac{2}{3}\right\}$

Question 17

Divide using long division.
-$\left(x^{2}+2 x-35\right) \div(x+7)$

Accepted Answer

A)  $x^{2}-5$ 
B)  $x+5$ 
C)  $x^{2}+3 x-28$ 
D)  $x-5$ 
A)  $x^{2}-5$ 
B)  $x+5$ 
C)  $x^{2}+3 x-28$ 
D)  $x-5$

Question 18

$-4 x^{2}\left(-2 x^{4}-5 x^{2}-4\right)$

Accepted Answer

A)  $8 x^{6}+20 x^{4}+16 x^{2}$ 
B)  $8 x^{6}-5 x^{2}-4$ 
C)  $8 x^{6}+20 x^{4}$ 
D)  $8 x^{4}+20 x^{2}+16$ 
A)  $8 x^{6}+20 x^{4}+16 x^{2}$ 
B)  $8 x^{6}-5 x^{2}-4$ 
C)  $8 x^{6}+20 x^{4}$ 
D)  $8 x^{4}+20 x^{2}+16$

Question 19

Divide. Assume all variables are nonzero
-$\left(x^{4} y^{4}-x^{3} y^{2}-x^{2} y\right) \div\left(x^{2} y\right)$

Accepted Answer

A)  $x^{2} y^{3}-x y-1$ 
B)  $x^{2} y^{4}-x y^{2}-1$ 
C)  $x^{2} y^{3}-x y^{2}-y$ 
D)  $x^{2} y^{4}-x y-y$ 
A)  $x^{2} y^{3}-x y-1$ 
B)  $x^{2} y^{4}-x y^{2}-1$ 
C)  $x^{2} y^{3}-x y^{2}-y$ 
D)  $x^{2} y^{4}-x y-y$

Question 20

Identify the polynomial as a 
-$18 x^{4}-8$

Accepted Answer

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

Factor completely. If the polynomial cannot be factored, write "prime." - $9 x^{2}+64$

Divide. Assume all variables are nonzero - $\frac{30 x^{5}-15 x^{2}+50 x}{5 x}$

Find the missing factor or exponent(s). - $\frac{x^{10} y^{2} ?}{x^{?} y^{19}}=x^{4} y^{6}$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $-5 x^{4}-14 x^{2}+7 x+6 x^{6}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+5 x+4$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4} y^{5}-x^{3} y^{7}$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(7 x^{2}\right)^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{2}+4 x-24$

Divide. Assume all variables are nonzero - $\frac{12 x^{8}+6 x^{6}}{3 x^{4}}$

Factor by grouping. - $15 x^{2}-9 x-10 x+6$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(3 x^{2} y^{3}\right)^{2}$

If the distance from the earth to the sun were $92,900,000$ miles, how long would it take a rocket, traveling at $3.8 \times 10^{3}$ miles per hour, to reach the sun? Round to three decimal places.

$x(x+13)=0$

Divide. Assume all variables are nonzero - $\frac{10 x^{10}}{5 x^{8}}$

Evaluate the given function - $f(x)=x^{3}, f(-5)$

$12 x^{2}+23 x+10=0$

Divide using long division. - $\left(x^{2}+2 x-35\right) \div(x+7)$

$-4 x^{2}\left(-2 x^{4}-5 x^{2}-4\right)$

Divide. Assume all variables are nonzero - $\left(x^{4} y^{4}-x^{3} y^{2}-x^{2} y\right) \div\left(x^{2} y\right)$

Identify the polynomial as a - $18 x^{4}-8$

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

Factor completely. If the polynomial cannot be factored, write "prime." - 9x2+649 x^{2}+649x2+64

Divide. Assume all variables are nonzero - 30x5−15x2+50x5x\frac{30 x^{5}-15 x^{2}+50 x}{5 x}5x30x5−15x2+50x​

Find the missing factor or exponent(s). - x10y2?x?y19=x4y6\frac{x^{10} y^{2} ?}{x^{?} y^{19}}=x^{4} y^{6}x?y19x10y2?​=x4y6

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - −5x4−14x2+7x+6x6-5 x^{4}-14 x^{2}+7 x+6 x^{6}−5x4−14x2+7x+6x6

Factor completely. If the polynomial cannot be factored, write "prime." - x2+5x+4x^{2}+5 x+4x2+5x+4

Factor completely. If the polynomial cannot be factored, write "prime." - x4y5−x3y7x^{4} y^{5}-x^{3} y^{7}x4y5−x3y7

Choose the one alternative that best completes the statement or answers thequestion. - (7x2)2\left(7 x^{2}\right)^{2}(7x2)2

Factor completely. If the polynomial cannot be factored, write "prime." - 4x2+4x−244 x^{2}+4 x-244x2+4x−24

Divide. Assume all variables are nonzero - 12x8+6x63x4\frac{12 x^{8}+6 x^{6}}{3 x^{4}}3x412x8+6x6​

Factor by grouping. - 15x2−9x−10x+615 x^{2}-9 x-10 x+615x2−9x−10x+6

Choose the one alternative that best completes the statement or answers thequestion. - (3x2y3)2\left(3 x^{2} y^{3}\right)^{2}(3x2y3)2

If the distance from the earth to the sun were 92,900,00092,900,00092,900,000 miles, how long would it take a rocket, traveling at 3.8×1033.8 \times 10^{3}3.8×103 miles per hour, to reach the sun? Round to three decimal places.

x(x+13)=0x(x+13)=0x(x+13)=0

Divide. Assume all variables are nonzero - 10x105x8\frac{10 x^{10}}{5 x^{8}}5x810x10​

Evaluate the given function - f(x)=x3,f(−5)f(x)=x^{3}, f(-5)f(x)=x3,f(−5)

12x2+23x+10=012 x^{2}+23 x+10=012x2+23x+10=0

Divide using long division. - (x2+2x−35)÷(x+7)\left(x^{2}+2 x-35\right) \div(x+7)(x2+2x−35)÷(x+7)

−4x2(−2x4−5x2−4)-4 x^{2}\left(-2 x^{4}-5 x^{2}-4\right)−4x2(−2x4−5x2−4)

Divide. Assume all variables are nonzero - (x4y4−x3y2−x2y)÷(x2y)\left(x^{4} y^{4}-x^{3} y^{2}-x^{2} y\right) \div\left(x^{2} y\right)(x4y4−x3y2−x2y)÷(x2y)

Identify the polynomial as a - 18x4−818 x^{4}-818x4−8

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

Factor completely. If the polynomial cannot be factored, write "prime." - $9 x^{2}+64$

Divide. Assume all variables are nonzero - $\frac{30 x^{5}-15 x^{2}+50 x}{5 x}$

Find the missing factor or exponent(s). - $\frac{x^{10} y^{2} ?}{x^{?} y^{19}}=x^{4} y^{6}$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $-5 x^{4}-14 x^{2}+7 x+6 x^{6}$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{2}+5 x+4$

Factor completely. If the polynomial cannot be factored, write "prime." - $x^{4} y^{5}-x^{3} y^{7}$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(7 x^{2}\right)^{2}$

Factor completely. If the polynomial cannot be factored, write "prime." - $4 x^{2}+4 x-24$

Divide. Assume all variables are nonzero - $\frac{12 x^{8}+6 x^{6}}{3 x^{4}}$

Factor by grouping. - $15 x^{2}-9 x-10 x+6$

Choose the one alternative that best completes the statement or answers thequestion. - $\left(3 x^{2} y^{3}\right)^{2}$

If the distance from the earth to the sun were $92,900,000$ miles, how long would it take a rocket, traveling at $3.8 \times 10^{3}$ miles per hour, to reach the sun? Round to three decimal places.

$x(x+13)=0$

Divide. Assume all variables are nonzero - $\frac{10 x^{10}}{5 x^{8}}$

Evaluate the given function - $f(x)=x^{3}, f(-5)$

$12 x^{2}+23 x+10=0$

Divide using long division. - $\left(x^{2}+2 x-35\right) \div(x+7)$

$-4 x^{2}\left(-2 x^{4}-5 x^{2}-4\right)$

Divide. Assume all variables are nonzero - $\left(x^{4} y^{4}-x^{3} y^{2}-x^{2} y\right) \div\left(x^{2} y\right)$

Identify the polynomial as a - $18 x^{4}-8$