Question 1

Simplify the expression. Write the result using positive exponents only.
-$- 3 z ^ { - 2 }$

Accepted Answer

A)  $\frac { 9 } { z ^ { 2 } }$ 
B)  $- \frac { 1 } { 9 z ^ { 2 } }$ 
C)  $\frac { 1 } { 9 z ^ { 2 } }$ 
D)  $- \frac { 3 } { \mathrm { z } ^ { 2 } }$ 
A)  $\frac { 9 } { z ^ { 2 } }$ 
B)  $- \frac { 1 } { 9 z ^ { 2 } }$ 
C)  $\frac { 1 } { 9 z ^ { 2 } }$ 
D)  $- \frac { 3 } { \mathrm { z } ^ { 2 } }$ D

Question 2

Use the quotient rule to simplify the expression.
-$\frac { \mathrm { s } ^ { 12 } \mathrm { t } ^ { 9 } } { \mathrm {~s} ^ { 2 } \mathrm { t } }$

Accepted Answer

A)  $\mathrm { s } ^ { 14 } \mathrm { t }^{ 10}$ 
B)  $\mathrm { s } ^ { 10 } \mathrm { t } ^ { 7 }$ 
C)  $s ^ { 10 } t ^ { 8 }$ 
D)  $\mathrm { s } ^ { 10 } \mathrm { t } ^ { 9 }$ 
A)  $\mathrm { s } ^ { 14 } \mathrm { t }^{ 10}$ 
B)  $\mathrm { s } ^ { 10 } \mathrm { t } ^ { 7 }$ 
C)  $s ^ { 10 } t ^ { 8 }$ 
D)  $\mathrm { s } ^ { 10 } \mathrm { t } ^ { 9 }$ C

Question 3

Simplify the expression. Write the result using positive exponents only.
-$\frac { 1 } { m ^ { - 6 } }$

Accepted Answer

A)  $- \mathrm { m } ^ { 1 / 6 }$ 
B)  $m ^ { 1 / 6 }$ 
C)  $- m ^ { 6 }$ 
D)  $\mathrm { m } ^ { 6 }$ 
A)  $- \mathrm { m } ^ { 1 / 6 }$ 
B)  $m ^ { 1 / 6 }$ 
C)  $- m ^ { 6 }$ 
D)  $\mathrm { m } ^ { 6 }$ D

Question 4

Perform the indicated operation.
-Subtract $( 3 x + 3 )$ from the sum of $\left( 9 x ^ { 2 } + 8 x + 1 \right)$ and $\left( x ^ { 3 } - 2 \right)$.

Accepted Answer

A)  $x ^ { 3 } - 9 x ^ { 2 } - 5 x - 4$ 
B)  $- x ^ { 3 } - 9 x ^ { 2 } - 5 x + 4$ 
C)  $x ^ { 3 } - 9 x ^ { 2 } - 5 x + 4$ 
D)  $x ^ { 3 } + 9 x ^ { 2 } + 5 x - 4$ 
A)  $x ^ { 3 } - 9 x ^ { 2 } - 5 x - 4$ 
B)  $- x ^ { 3 } - 9 x ^ { 2 } - 5 x + 4$ 
C)  $x ^ { 3 } - 9 x ^ { 2 } - 5 x + 4$ 
D)  $x ^ { 3 } + 9 x ^ { 2 } + 5 x - 4$

Question 5

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of
these.
-$- 15 z ^ { 4 } + 5 z ^ { 3 } - 7 z ^ { 2 } + 9$

Accepted Answer

A)  4; trinomial 
B)  10; binomial 
C)  9; trinomial 
D)  4; none of these 
A)  4; trinomial 
B)  10; binomial 
C)  9; trinomial 
D)  4; none of these

Question 6

Perform the division.
-$\frac { 12 x ^ { 7 } - 28 x ^ { 5 } } { 4 x ^ { 3 } }$

Accepted Answer

A)  $- 4 x ^ { 9 }$ 
B)  $12 x ^ { 7 } - 7 x ^ { 2 }$ 
C)  $3 x ^ { 4 } - 7 x ^ { 2 }$ 
D)  $3 x ^ { 4 } - 28 x ^ { 5 }$ 
A)  $- 4 x ^ { 9 }$ 
B)  $12 x ^ { 7 } - 7 x ^ { 2 }$ 
C)  $3 x ^ { 4 } - 7 x ^ { 2 }$ 
D)  $3 x ^ { 4 } - 28 x ^ { 5 }$

Question 7

Evaluate the expression.
-$( - 5 ) ^ { 3 }$

Accepted Answer

A)  -15 
B)  15 
C)  -125 
D)  125 
A)  -15 
B)  15 
C)  -125 
D)  125

Question 8

Use synthetic division to divide.
-$\left( 49 x ^ { 3 } + 49 x ^ { 2 } + 13 x - 6 \right) \div \left( x + \frac { 4 } { 7 } \right)$

Accepted Answer

A)  $49 x ^ { 2 } + 21 x + 1 - \frac { 46 } { 7 x + 4 }$ 
B)  $49 x ^ { 2 } + 21 x + 1 - \frac { 10 } { x + \frac { 4 } { 7 } }$ 
C)  $49 x ^ { 2 } + 21 x + 1 + \frac { 10 } { x + \frac { 4 } { 7 } }$ 
D)  $49 x ^ { 2 } + 21 x + 1 + \frac { 46 } { 7 x + 4 }$ 
A)  $49 x ^ { 2 } + 21 x + 1 - \frac { 46 } { 7 x + 4 }$ 
B)  $49 x ^ { 2 } + 21 x + 1 - \frac { 10 } { x + \frac { 4 } { 7 } }$ 
C)  $49 x ^ { 2 } + 21 x + 1 + \frac { 10 } { x + \frac { 4 } { 7 } }$ 
D)  $49 x ^ { 2 } + 21 x + 1 + \frac { 46 } { 7 x + 4 }$

Question 9

Write the number in scientific notation.
-In the metric system of measurement, the prefix mega- means $1,000,000$. Write this number in scientific notation.

Accepted Answer

A)  $0.1 \times 10 ^ { - 5 }$ 
B)  $1 \times 10 ^ { 6 }$ 
C)  $10 \times 10 ^ { 5 }$ 
D)  $1 \times 10 ^ { - 6 }$ 
A)  $0.1 \times 10 ^ { - 5 }$ 
B)  $1 \times 10 ^ { 6 }$ 
C)  $10 \times 10 ^ { 5 }$ 
D)  $1 \times 10 ^ { - 6 }$

Question 10

Simplify the expression. Write the result using positive exponents only.
-$\left( - 2 x ^ { 5 } y ^ { - 6 } \right) \left( 5 x ^ { - 1 } y \right)$

Accepted Answer

A)  $\frac { - 10 x ^ { 4 } } { y ^ { 5 } }$ 
B)  $\frac { - 10 x ^ { 6 } } { y ^ { 7 } }$ 
C)  $\frac { 3 x ^ { 4 } } { y ^ { 5 } }$ 
D)  $- 10 x ^ { 4 } y ^ { 7 }$ 
A)  $\frac { - 10 x ^ { 4 } } { y ^ { 5 } }$ 
B)  $\frac { - 10 x ^ { 6 } } { y ^ { 7 } }$ 
C)  $\frac { 3 x ^ { 4 } } { y ^ { 5 } }$ 
D)  $- 10 x ^ { 4 } y ^ { 7 }$

Question 11

Find the quotient using long division.
-$\frac { x ^ { 2 } + 10 x + 12 } { x + 7 }$

Accepted Answer

A)  $x + 4$ 
B)  $\frac { x + 3 } { x + 7 }$ 
C)  $x + 3 + \frac { 9 } { x + 7 }$ 
D)  $x + 3 - \frac { 9 } { x + 7 }$ 
A)  $x + 4$ 
B)  $\frac { x + 3 } { x + 7 }$ 
C)  $x + 3 + \frac { 9 } { x + 7 }$ 
D)  $x + 3 - \frac { 9 } { x + 7 }$

Question 12

Multiply using the FOIL method.
-$( b - 2 ) ( b - 3 )$

Accepted Answer

A)  $2 b ^ { 2 } - 6$ 
B)  $b ^ { 2 } - 5 b + 6$ 
C)  $b ^ { 2 } + 5 b - 6$ 
D)  $2 b + 6$ 
A)  $2 b ^ { 2 } - 6$ 
B)  $b ^ { 2 } - 5 b + 6$ 
C)  $b ^ { 2 } + 5 b - 6$ 
D)  $2 b + 6$

Question 13

Use the power rule to simplify the expression.
-$\left( 5 ^ { 3 } \right) ^ { 5 }$

Accepted Answer

A)  $5 ^ { 8 }$ 
B)  $25 ^ { 15 }$ 
C)  $5 ^ { 15 }$ 
D)  $25 ^ { 3 }$ 
A)  $5 ^ { 8 }$ 
B)  $25 ^ { 15 }$ 
C)  $5 ^ { 15 }$ 
D)  $25 ^ { 3 }$

Question 14

Simplify.
-If $Q ( x ) = 3 x ^ { 2 } + 7 x - 6$, find $Q ( - 1 )$

Accepted Answer

A)  $- 16$ 
B)  $- 10$ 
C)  $- 2$ 
D)  4 
A)  $- 16$ 
B)  $- 10$ 
C)  $- 2$ 
D)  4

Question 15

Multiply.
-$( 9 p + 7 ) ( 9 p - 7 )$

Accepted Answer

A)  $81 p ^ { 2 } - 49$ 
B)  $81 p ^ { 2 } + 126 p - 49$ 
C)  $p ^ { 2 } - 49$ 
D)  $81 p ^ { 2 } - 126 p - 49$ 
A)  $81 p ^ { 2 } - 49$ 
B)  $81 p ^ { 2 } + 126 p - 49$ 
C)  $p ^ { 2 } - 49$ 
D)  $81 p ^ { 2 } - 126 p - 49$

Question 16

Multiply.
-$\left( 12 + \frac { 1 } { 10 } z \right) \left( 12 - \frac { 1 } { 10 } z \right)$

Accepted Answer

A)  $144 - \frac { 12 } { 5 } z - \frac { 1 } { 100 } z ^ { 2 }$ 
B)  $144 - \frac { 1 } { 100 } \mathrm { z } ^ { 2 }$ 
C)  $144 + \frac { 12 } { 5 } z - \frac { 1 } { 100 } z ^ { 2 }$ 
D)  $144 - \frac { 1 } { 5 } z ^ { 2 }$ 
A)  $144 - \frac { 12 } { 5 } z - \frac { 1 } { 100 } z ^ { 2 }$ 
B)  $144 - \frac { 1 } { 100 } \mathrm { z } ^ { 2 }$ 
C)  $144 + \frac { 12 } { 5 } z - \frac { 1 } { 100 } z ^ { 2 }$ 
D)  $144 - \frac { 1 } { 5 } z ^ { 2 }$

Question 17

Multiply.
-$( p + 13 q ) ( p - 13 q )$

Accepted Answer

A)  $p ^ { 2 } + 26 p q - 169 q ^ { 2 }$ 
B)  $p ^ { 2 } - 26 p q - 169 q ^ { 2 }$ 
C)  $p ^ { 2 } - 26 q ^ { 2 }$ 
D)  $p ^ { 2 } - 169 q ^ { 2 }$ 
A)  $p ^ { 2 } + 26 p q - 169 q ^ { 2 }$ 
B)  $p ^ { 2 } - 26 p q - 169 q ^ { 2 }$ 
C)  $p ^ { 2 } - 26 q ^ { 2 }$ 
D)  $p ^ { 2 } - 169 q ^ { 2 }$

Question 18

Solve.
-If $P ( x ) = x ^ { 5 } - 7 x ^ { 4 } + 4 x ^ { 3 } - 5$, use the remainder theorem to find $P ( 2 )$.

Accepted Answer

A)  $- 17$ 
B)  $- 85$ 
C)  $- 53$ 
D)  53 
A)  $- 17$ 
B)  $- 85$ 
C)  $- 53$ 
D)  53

Question 19

Evaluate the expression with the given replacement values.
-$- 6 x ^ { 3 } y ; x = 4$ and $y = - 2$

Accepted Answer

A)  144 
B)  192 
C)  768 
D)  $- 768$ 
A)  144 
B)  192 
C)  768 
D)  $- 768$

Question 20

Perform the indicated operation.
-Subtract $( 3 x - 30 )$ from the sum of $( - 2 x + 7 )$ and $( 9 x - 1 )$.

Accepted Answer

A)  $8 x + 38$ 
B)  $10 x - 24$ 
C)  $- 4 x - 36$ 
D)  $4 x + 36$ 
A)  $8 x + 38$ 
B)  $10 x - 24$ 
C)  $- 4 x - 36$ 
D)  $4 x + 36$

Simplify the expression. Write the result using positive exponents only. - $- 3 z ^ { - 2 }$

Use the quotient rule to simplify the expression. - $\frac { \mathrm { s } ^ { 12 } \mathrm { t } ^ { 9 } } { \mathrm {~s} ^ { 2 } \mathrm { t } }$

Simplify the expression. Write the result using positive exponents only. - $\frac { 1 } { m ^ { - 6 } }$

Perform the indicated operation. -Subtract $( 3 x + 3 )$ from the sum of $\left( 9 x ^ { 2 } + 8 x + 1 \right)$ and $\left( x ^ { 3 } - 2 \right)$ .

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $- 15 z ^ { 4 } + 5 z ^ { 3 } - 7 z ^ { 2 } + 9$

Perform the division. - $\frac { 12 x ^ { 7 } - 28 x ^ { 5 } } { 4 x ^ { 3 } }$

Evaluate the expression. - $( - 5 ) ^ { 3 }$

Use synthetic division to divide. - $\left( 49 x ^ { 3 } + 49 x ^ { 2 } + 13 x - 6 \right) \div \left( x + \frac { 4 } { 7 } \right)$

Write the number in scientific notation. -In the metric system of measurement, the prefix mega- means $1,000,000$ . Write this number in scientific notation.

Simplify the expression. Write the result using positive exponents only. - $\left( - 2 x ^ { 5 } y ^ { - 6 } \right) \left( 5 x ^ { - 1 } y \right)$

Find the quotient using long division. - $\frac { x ^ { 2 } + 10 x + 12 } { x + 7 }$

Multiply using the FOIL method. - $( b - 2 ) ( b - 3 )$

Use the power rule to simplify the expression. - $\left( 5 ^ { 3 } \right) ^ { 5 }$

Simplify. -If $Q ( x ) = 3 x ^ { 2 } + 7 x - 6$ , find $Q ( - 1 )$

Multiply. - $( 9 p + 7 ) ( 9 p - 7 )$

Multiply. - $\left( 12 + \frac { 1 } { 10 } z \right) \left( 12 - \frac { 1 } { 10 } z \right)$

Multiply. - $( p + 13 q ) ( p - 13 q )$

Solve. -If $P ( x ) = x ^ { 5 } - 7 x ^ { 4 } + 4 x ^ { 3 } - 5$ , use the remainder theorem to find $P ( 2 )$ .

Evaluate the expression with the given replacement values. - $- 6 x ^ { 3 } y ; x = 4$ and $y = - 2$

Perform the indicated operation. -Subtract $( 3 x - 30 )$ from the sum of $( - 2 x + 7 )$ and $( 9 x - 1 )$ .

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Simplify the expression. Write the result using positive exponents only. - −3z−2- 3 z ^ { - 2 }−3z−2

Use the quotient rule to simplify the expression. - s12t9 s2t\frac { \mathrm { s } ^ { 12 } \mathrm { t } ^ { 9 } } { \mathrm {~s} ^ { 2 } \mathrm { t } } s2ts12t9​

Simplify the expression. Write the result using positive exponents only. - 1m−6\frac { 1 } { m ^ { - 6 } }m−61​

Perform the indicated operation. -Subtract (3x+3)( 3 x + 3 )(3x+3) from the sum of (9x2+8x+1)\left( 9 x ^ { 2 } + 8 x + 1 \right)(9x2+8x+1) and (x3−2)\left( x ^ { 3 } - 2 \right)(x3−2) .

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - −15z4+5z3−7z2+9- 15 z ^ { 4 } + 5 z ^ { 3 } - 7 z ^ { 2 } + 9−15z4+5z3−7z2+9

Perform the division. - 12x7−28x54x3\frac { 12 x ^ { 7 } - 28 x ^ { 5 } } { 4 x ^ { 3 } }4x312x7−28x5​

Evaluate the expression. - (−5)3( - 5 ) ^ { 3 }(−5)3

Use synthetic division to divide. - (49x3+49x2+13x−6)÷(x+47)\left( 49 x ^ { 3 } + 49 x ^ { 2 } + 13 x - 6 \right) \div \left( x + \frac { 4 } { 7 } \right)(49x3+49x2+13x−6)÷(x+74​)

Write the number in scientific notation. -In the metric system of measurement, the prefix mega- means 1,000,0001,000,0001,000,000 . Write this number in scientific notation.

Simplify the expression. Write the result using positive exponents only. - (−2x5y−6)(5x−1y)\left( - 2 x ^ { 5 } y ^ { - 6 } \right) \left( 5 x ^ { - 1 } y \right)(−2x5y−6)(5x−1y)

Find the quotient using long division. - x2+10x+12x+7\frac { x ^ { 2 } + 10 x + 12 } { x + 7 }x+7x2+10x+12​

Multiply using the FOIL method. - (b−2)(b−3)( b - 2 ) ( b - 3 )(b−2)(b−3)

Use the power rule to simplify the expression. - (53)5\left( 5 ^ { 3 } \right) ^ { 5 }(53)5

Simplify. -If Q(x)=3x2+7x−6Q ( x ) = 3 x ^ { 2 } + 7 x - 6Q(x)=3x2+7x−6 , find Q(−1)Q ( - 1 )Q(−1)

Multiply. - (9p+7)(9p−7)( 9 p + 7 ) ( 9 p - 7 )(9p+7)(9p−7)

Multiply. - (12+110z)(12−110z)\left( 12 + \frac { 1 } { 10 } z \right) \left( 12 - \frac { 1 } { 10 } z \right)(12+101​z)(12−101​z)

Multiply. - (p+13q)(p−13q)( p + 13 q ) ( p - 13 q )(p+13q)(p−13q)

Solve. -If P(x)=x5−7x4+4x3−5P ( x ) = x ^ { 5 } - 7 x ^ { 4 } + 4 x ^ { 3 } - 5P(x)=x5−7x4+4x3−5 , use the remainder theorem to find P(2)P ( 2 )P(2) .

Evaluate the expression with the given replacement values. - −6x3y;x=4- 6 x ^ { 3 } y ; x = 4−6x3y;x=4 and y=−2y = - 2y=−2

Perform the indicated operation. -Subtract (3x−30)( 3 x - 30 )(3x−30) from the sum of (−2x+7)( - 2 x + 7 )(−2x+7) and (9x−1)( 9 x - 1 )(9x−1) .