Question 1

Simplify the expression. Write your answer with positive exponents only. $$\left( t ^ { 3 } z \right) ^ { 2 } \left( 3 t ^ { 2 } z ^ { 4 } \right) ^ { - 2 }$$

Accepted Answer

A)  $\frac { t ^ { 10 } } { 9 z ^ { 6 } }$ 
B)  $\frac { 1 } { 81 t ^ { 4 } z ^ { 20 } }$ 
C)  $\frac { z ^ { 7 } t } { 9 }$ 
D)  $\frac { 9 z ^ { 10 } } { t }$ 
A)  $\frac { t ^ { 10 } } { 9 z ^ { 6 } }$ 
B)  $\frac { 1 } { 81 t ^ { 4 } z ^ { 20 } }$ 
C)  $\frac { z ^ { 7 } t } { 9 }$ 
D)  $\frac { 9 z ^ { 10 } } { t }$

Question 2

The following table represents the result of a synthetic division.

Use $x$ as the variable. Identify the quotient.

Accepted Answer

A)  $2 x ^ { 3 } - 6 x ^ { 2 } - 5 x + 9$ 
B)  $2 x ^ { 2 } - 2 x - 9$ 
C)  $x - 2$ 
D)  $x + 2$ 
A)  $2 x ^ { 3 } - 6 x ^ { 2 } - 5 x + 9$ 
B)  $2 x ^ { 2 } - 2 x - 9$ 
C)  $x - 2$ 
D)  $x + 2$

Question 3

How many miles (to the nearest hundredth of a mile) is a trip that is $1.1 \times 10 ^ { 6 }$ inches?

Accepted Answer

A)  34.72 miles 
B)  17.36 miles 
C)  8.68 miles 
D)  1736.11 miles 
A)  34.72 miles 
B)  17.36 miles 
C)  8.68 miles 
D)  1736.11 miles

Question 4

Write an expression for the volume and simplify your answer.

[The figure is not necessarily drawn to scale.]

Accepted Answer

A)  $3 x ^ { 3 } + 11 x ^ { 2 } + 30 x$ 
B)  $3 x ^ { 3 } + 90 x$ 
C)  $3 x ^ { 3 } + 33 x + 90$ 
D)  $3 x ^ { 3 } + 33 x ^ { 2 } + 90 x$ 
A)  $3 x ^ { 3 } + 11 x ^ { 2 } + 30 x$ 
B)  $3 x ^ { 3 } + 90 x$ 
C)  $3 x ^ { 3 } + 33 x + 90$ 
D)  $3 x ^ { 3 } + 33 x ^ { 2 } + 90 x$

Question 5

Multiply by using the special case products. $$\left( - 2 r ^ { 2 } + 2 s \right) ^ { 2 }$$

Accepted Answer

A)  $4 r ^ { 4 } - 8 r ^ { 2 } s + 4 s ^ { 2 }$ 
B)  $4 r ^ { 4 } - 4 s ^ { 2 }$ 
C)  $4 r ^ { 4 } + 4 s ^ { 2 }$ 
D)  $4 r ^ { 4 } - 8 r s + 4 s ^ { 2 }$ 
A)  $4 r ^ { 4 } - 8 r ^ { 2 } s + 4 s ^ { 2 }$ 
B)  $4 r ^ { 4 } - 4 s ^ { 2 }$ 
C)  $4 r ^ { 4 } + 4 s ^ { 2 }$ 
D)  $4 r ^ { 4 } - 8 r s + 4 s ^ { 2 }$

Question 6

Choose the polynomial that is described. A monomial in one variable of degree 4

Accepted Answer

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

Question 7

Divide by using synthetic division. $$\left( - 2 w ^ { 3 } + 11 w ^ { 2 } - 10 w - 4 \right) \div ( w - 1 )$$

Accepted Answer

A)  $- 2 w ^ { 2 } + 9 w - 1$ 
B)  $- 2 w ^ { 2 } + 9 w + 1$ 
C)  $- 2 w ^ { 2 } - 2 w - 23 + \frac { 19 } { w + 1 }$ 
D)  $- 2 w ^ { 2 } + 9 w - 1 - \frac { 5 } { w - 1 }$ 
A)  $- 2 w ^ { 2 } + 9 w - 1$ 
B)  $- 2 w ^ { 2 } + 9 w + 1$ 
C)  $- 2 w ^ { 2 } - 2 w - 23 + \frac { 19 } { w + 1 }$ 
D)  $- 2 w ^ { 2 } + 9 w - 1 - \frac { 5 } { w - 1 }$

Question 8

Divide the polynomials by using long division. $$\left( 8 p ^ { 4 } - 31 p ^ { 2 } - 43 \right) \div \left( p ^ { 2 } - 5 \right)$$

Accepted Answer

A)  $8 p ^ { 2 } + 9 + \frac { 2 } { p ^ { 2 } - 5 }$ 
B)  $8 p ^ { 2 } + 9 - \frac { 2 } { p ^ { 2 } - 5 }$ 
C)  $8 p ^ { 2 } - \frac { 2 p } { p ^ { 2 } - 5 }$ 
D)  $8 p ^ { 2 } + 9 p + 2$ 
A)  $8 p ^ { 2 } + 9 + \frac { 2 } { p ^ { 2 } - 5 }$ 
B)  $8 p ^ { 2 } + 9 - \frac { 2 } { p ^ { 2 } - 5 }$ 
C)  $8 p ^ { 2 } - \frac { 2 p } { p ^ { 2 } - 5 }$ 
D)  $8 p ^ { 2 } + 9 p + 2$

Question 9

Write the opposite of the given polynomial. $- 7 x ^ { 2 } - 4 x$

Accepted Answer

A)  $- 4 x - 7 x ^ { 2 }$ 
B)  $7 x ^ { 2 } + 4 x$ 
C)  $7 x ^ { 2 } - 4 x$ 
D)  $7 x ^ { - 2 } + 4 x$ 
A)  $- 4 x - 7 x ^ { 2 }$ 
B)  $7 x ^ { 2 } + 4 x$ 
C)  $7 x ^ { 2 } - 4 x$ 
D)  $7 x ^ { - 2 } + 4 x$

Question 10

Simplify. $$\left( \frac { 5 } { 8 } \right) ^ { - 2 }$$

Accepted Answer

A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 64 } { 25 }$ 
C)  $- \frac { 25 } { 64 }$ 
D)  $- \frac { 5 } { 4 }$ 
A)  $\frac { 1 } { 2 }$ 
B)  $\frac { 64 } { 25 }$ 
C)  $- \frac { 25 } { 64 }$ 
D)  $- \frac { 5 } { 4 }$

Question 11

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. $$k ( x ) = - 3 x ^ { 6 } - 0.7 x + x ^ { 3 }$$

Accepted Answer

A)  No, some range elements correspond to more than one domain element 
B)  Yes; degree 6 
C)  Yes; degree 10 
D)  No; -0.7 is not an integer 
A)  No, some range elements correspond to more than one domain element 
B)  Yes; degree 6 
C)  Yes; degree 10 
D)  No; -0.7 is not an integer

Question 12

Factor the binomial or identify it as prime $27 q ^ { 2 } - 48 r ^ { 2 }$

Accepted Answer

A)  $3 ( 3 q + 4 r ) ^ { 2 }$ 
B)  $3 \left( 9 q ^ { 2 } - 16 r ^ { 2 } \right)$ 
C)  $3 ( 3 q + 4 r ) ( 3 q - 4 r )$ 
D)  Prime 
A)  $3 ( 3 q + 4 r ) ^ { 2 }$ 
B)  $3 \left( 9 q ^ { 2 } - 16 r ^ { 2 } \right)$ 
C)  $3 ( 3 q + 4 r ) ( 3 q - 4 r )$ 
D)  Prime

Question 13

Divide the polynomials by using an appropriate method. $$\left( 8 y ^ { 3 } - 4 y ^ { 2 } - 5 y + 5 \right) \div ( y - 1 )$$

Accepted Answer

A)  $8 y ^ { 2 } + 8 y + 7 - \frac { 2 } { y + 1 }$ 
B)  $8 y ^ { 2 } + 4 y - 1 + \frac { 4 } { y - 1 }$ 
C)  $8 y ^ { 2 } + 4 y - 1$ 
D)  $8 y ^ { 2 } + 4 y + 1$ 
A)  $8 y ^ { 2 } + 8 y + 7 - \frac { 2 } { y + 1 }$ 
B)  $8 y ^ { 2 } + 4 y - 1 + \frac { 4 } { y - 1 }$ 
C)  $8 y ^ { 2 } + 4 y - 1$ 
D)  $8 y ^ { 2 } + 4 y + 1$

Question 14

Factor the expression that defines the function. $$P ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 24 x ^ { 2 }$$

Accepted Answer

A)  $P ( x ) = x ^ { 2 } \left( x ^ { 2 } - 6 \right) \left( x ^ { 2 } + 4 \right)$ 
B)  $P ( x ) = x ( x - 6 ) ( x + 4 )$ 
C)  $P ( x ) = x ^ { 2 } ( x - 6 ) ( x + 4 )$ 
D)  $P ( x ) = x ^ { 2 } ( x - 2 ) ( x - 24 )$ 
A)  $P ( x ) = x ^ { 2 } \left( x ^ { 2 } - 6 \right) \left( x ^ { 2 } + 4 \right)$ 
B)  $P ( x ) = x ( x - 6 ) ( x + 4 )$ 
C)  $P ( x ) = x ^ { 2 } ( x - 6 ) ( x + 4 )$ 
D)  $P ( x ) = x ^ { 2 } ( x - 2 ) ( x - 24 )$

Question 15

Factor the binomial or identify it as prime. $25 y ^ { 2 } + 9$

Accepted Answer

A)  $( 5 y + 3 ) ( 5 y - 3 )$ 
B)  $( 5 y + 3 ) ^ { 2 }$ 
C)  $( 5 y - 3 ) ^ { 2 }$ 
D)  Prime 
A)  $( 5 y + 3 ) ( 5 y - 3 )$ 
B)  $( 5 y + 3 ) ^ { 2 }$ 
C)  $( 5 y - 3 ) ^ { 2 }$ 
D)  Prime

Question 16

Simplify the expression. $$( u - 1 ) ( u - 4 ) ( u + 5 )$$

Accepted Answer

A)  $u ^ { 3 } - 21 u + 20$ 
B)  $u ^ { 3 } + 1 u + 20$ 
C)  $u ^ { 3 } - 1 u ^ { 2 } - 21 u + 20$ 
D)  $u ^ { 3 } - 10 u ^ { 2 } - 21 u + 20$ 
A)  $u ^ { 3 } - 21 u + 20$ 
B)  $u ^ { 3 } + 1 u + 20$ 
C)  $u ^ { 3 } - 1 u ^ { 2 } - 21 u + 20$ 
D)  $u ^ { 3 } - 10 u ^ { 2 } - 21 u + 20$

Question 17

Divide the polynomials by using long division. $$\left( 14 x ^ { 2 } - 33 x - 5 \right) \div ( 7 x + 1 )$$

Accepted Answer

A)  $14 x ^ { 2 } - 33 x - \frac { 5 } { 7 x + 1 }$ 
B)  $2 x - 5$ 
C)  $2 x - \frac { 55 } { 7 }$ 
D)  $2 x + 5$ 
A)  $14 x ^ { 2 } - 33 x - \frac { 5 } { 7 x + 1 }$ 
B)  $2 x - 5$ 
C)  $2 x - \frac { 55 } { 7 }$ 
D)  $2 x + 5$

Question 18

Subtract the polynomials and simplify. $\begin{array}{rr}
-3 u^{3}+2 u^{2} & +1 \
-\left(-9 u^{3}+5 u^{2}-3 u\right. & -5)\\hline
\end{array}$

Accepted Answer

A)  $6 u ^ { 3 } - 3 u ^ { 2 } - 3 u + 6$ 
B)  $6 u ^ { 3 } + 7 u ^ { 2 } - 3 u - 4$ 
C)  $6 u ^ { 3 } - 3 u ^ { 2 } + 3 u + 6$ 
D)  $- 12 u ^ { 3 } + 7 u ^ { 2 } - 3 u - 4$ 
A)  $6 u ^ { 3 } - 3 u ^ { 2 } - 3 u + 6$ 
B)  $6 u ^ { 3 } + 7 u ^ { 2 } - 3 u - 4$ 
C)  $6 u ^ { 3 } - 3 u ^ { 2 } + 3 u + 6$ 
D)  $- 12 u ^ { 3 } + 7 u ^ { 2 } - 3 u - 4$

Question 19

Complete the property of exponents. $b ^ { n } \cdot b ^ { m } =$_____

Accepted Answer

A)  $b ^ { n } + b ^ { m }$ 
B)  $b ^ { n + m }$ 
C)  $b ^ { n - m }$ 
D)  $b ^ { n \cdot m }$ 
A)  $b ^ { n } + b ^ { m }$ 
B)  $b ^ { n + m }$ 
C)  $b ^ { n - m }$ 
D)  $b ^ { n \cdot m }$

Question 20

Factor the binomial or identify it as prime. $2 z ^ { 4 } - 2$

Accepted Answer

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

Simplify the expression. Write your answer with positive exponents only. $\left( t ^ { 3 } z \right) ^ { 2 } \left( 3 t ^ { 2 } z ^ { 4 } \right) ^ { - 2 }$

The following table represents the result of a synthetic division. Use $x$ as the variable. Identify the quotient.

How many miles (to the nearest hundredth of a mile) is a trip that is $1.1 \times 10 ^ { 6 }$ inches?

Write an expression for the volume and simplify your answer. [The figure is not necessarily drawn to scale.]

Multiply by using the special case products. $\left( - 2 r ^ { 2 } + 2 s \right) ^ { 2 }$

Choose the polynomial that is described. A monomial in one variable of degree 4

Divide by using synthetic division. $\left( - 2 w ^ { 3 } + 11 w ^ { 2 } - 10 w - 4 \right) \div ( w - 1 )$

Divide the polynomials by using long division. $\left( 8 p ^ { 4 } - 31 p ^ { 2 } - 43 \right) \div \left( p ^ { 2 } - 5 \right)$

Write the opposite of the given polynomial. $- 7 x ^ { 2 } - 4 x$

Simplify. $\left( \frac { 5 } { 8 } \right) ^ { - 2 }$

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. $k ( x ) = - 3 x ^ { 6 } - 0.7 x + x ^ { 3 }$

Factor the binomial or identify it as prime $27 q ^ { 2 } - 48 r ^ { 2 }$

Divide the polynomials by using an appropriate method. $\left( 8 y ^ { 3 } - 4 y ^ { 2 } - 5 y + 5 \right) \div ( y - 1 )$

Factor the expression that defines the function. $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 24 x ^ { 2 }$

Factor the binomial or identify it as prime. $25 y ^ { 2 } + 9$

Simplify the expression. $( u - 1 ) ( u - 4 ) ( u + 5 )$

Divide the polynomials by using long division. $\left( 14 x ^ { 2 } - 33 x - 5 \right) \div ( 7 x + 1 )$

Subtract the polynomials and simplify. -3+2 +1 - -9+5-3u -5)

Complete the property of exponents. $b ^ { n } \cdot b ^ { m } =$ _____

Factor the binomial or identify it as prime. $2 z ^ { 4 } - 2$

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

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Conic Sections

Binomial Expansions, Sequences, and Series

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Exam 4: Polynomials

Simplify the expression. Write your answer with positive exponents only. (t3z)2(3t2z4)−2\left( t ^ { 3 } z \right) ^ { 2 } \left( 3 t ^ { 2 } z ^ { 4 } \right) ^ { - 2 }(t3z)2(3t2z4)−2

The following table represents the result of a synthetic division. Use xxx as the variable. Identify the quotient.

How many miles (to the nearest hundredth of a mile) is a trip that is 1.1×1061.1 \times 10 ^ { 6 }1.1×106 inches?

Write an expression for the volume and simplify your answer. [The figure is not necessarily drawn to scale.]

Multiply by using the special case products. (−2r2+2s)2\left( - 2 r ^ { 2 } + 2 s \right) ^ { 2 }(−2r2+2s)2

Choose the polynomial that is described. A monomial in one variable of degree 4

Divide by using synthetic division. (−2w3+11w2−10w−4)÷(w−1)\left( - 2 w ^ { 3 } + 11 w ^ { 2 } - 10 w - 4 \right) \div ( w - 1 )(−2w3+11w2−10w−4)÷(w−1)

Divide the polynomials by using long division. (8p4−31p2−43)÷(p2−5)\left( 8 p ^ { 4 } - 31 p ^ { 2 } - 43 \right) \div \left( p ^ { 2 } - 5 \right)(8p4−31p2−43)÷(p2−5)

Write the opposite of the given polynomial. −7x2−4x- 7 x ^ { 2 } - 4 x−7x2−4x

Simplify. (58)−2\left( \frac { 5 } { 8 } \right) ^ { - 2 }(85​)−2

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. k(x)=−3x6−0.7x+x3k ( x ) = - 3 x ^ { 6 } - 0.7 x + x ^ { 3 }k(x)=−3x6−0.7x+x3

Factor the binomial or identify it as prime 27q2−48r227 q ^ { 2 } - 48 r ^ { 2 }27q2−48r2

Divide the polynomials by using an appropriate method. (8y3−4y2−5y+5)÷(y−1)\left( 8 y ^ { 3 } - 4 y ^ { 2 } - 5 y + 5 \right) \div ( y - 1 )(8y3−4y2−5y+5)÷(y−1)

Factor the expression that defines the function. P(x)=x4−2x3−24x2P ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 24 x ^ { 2 }P(x)=x4−2x3−24x2

Factor the binomial or identify it as prime. 25y2+925 y ^ { 2 } + 925y2+9

Simplify the expression. (u−1)(u−4)(u+5)( u - 1 ) ( u - 4 ) ( u + 5 )(u−1)(u−4)(u+5)

Divide the polynomials by using long division. (14x2−33x−5)÷(7x+1)\left( 14 x ^ { 2 } - 33 x - 5 \right) \div ( 7 x + 1 )(14x2−33x−5)÷(7x+1)

Subtract the polynomials and simplify. -3+2 +1 - -9+5-3u -5)

Complete the property of exponents. bn⋅bm=b ^ { n } \cdot b ^ { m } =bn⋅bm= _____

Factor the binomial or identify it as prime. 2z4−22 z ^ { 4 } - 22z4−2

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables and Functions

Systems of Linear Equations and Inequalities

Rational Expressions and Rational Equations

Radicals and Complex Numbers

Quadratic Equations, Functions and Inequalities

Exponential and Logarithmic Functions and Applications

Conic Sections

Binomial Expansions, Sequences, and Series

Online: Transformations, Piecewise-Defined Functions, and Probability

Filters

Simplify the expression. Write your answer with positive exponents only. $\left( t ^ { 3 } z \right) ^ { 2 } \left( 3 t ^ { 2 } z ^ { 4 } \right) ^ { - 2 }$

The following table represents the result of a synthetic division. Use $x$ as the variable. Identify the quotient.

How many miles (to the nearest hundredth of a mile) is a trip that is $1.1 \times 10 ^ { 6 }$ inches?

Multiply by using the special case products. $\left( - 2 r ^ { 2 } + 2 s \right) ^ { 2 }$

Divide by using synthetic division. $\left( - 2 w ^ { 3 } + 11 w ^ { 2 } - 10 w - 4 \right) \div ( w - 1 )$

Divide the polynomials by using long division. $\left( 8 p ^ { 4 } - 31 p ^ { 2 } - 43 \right) \div \left( p ^ { 2 } - 5 \right)$

Write the opposite of the given polynomial. $- 7 x ^ { 2 } - 4 x$

Simplify. $\left( \frac { 5 } { 8 } \right) ^ { - 2 }$

Determine whether the given function is a polynomial function. If it is a polynomial function, state the degree. If not, state the reason why. $k ( x ) = - 3 x ^ { 6 } - 0.7 x + x ^ { 3 }$

Factor the binomial or identify it as prime $27 q ^ { 2 } - 48 r ^ { 2 }$

Divide the polynomials by using an appropriate method. $\left( 8 y ^ { 3 } - 4 y ^ { 2 } - 5 y + 5 \right) \div ( y - 1 )$

Factor the expression that defines the function. $P ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 24 x ^ { 2 }$

Factor the binomial or identify it as prime. $25 y ^ { 2 } + 9$

Simplify the expression. $( u - 1 ) ( u - 4 ) ( u + 5 )$

Divide the polynomials by using long division. $\left( 14 x ^ { 2 } - 33 x - 5 \right) \div ( 7 x + 1 )$

Complete the property of exponents. $b ^ { n } \cdot b ^ { m } =$ _____

Factor the binomial or identify it as prime. $2 z ^ { 4 } - 2$