Question 1

Multiply using the FOIL method.
-$( x + 5 ) \left( x ^ { 2 } - 3 \right)$

Accepted Answer

A)  $5 x ^ { 2 } + x - 15$ 
B)  $x ^ { 3 } - 3 x ^ { 2 } + 5 x - 15$ 
C)  $x ^ { 3 } + 5 x ^ { 2 } - 3 x - 15$ 
D)  $x ^ { 2 } + 2 x - 15$ 
A)  $5 x ^ { 2 } + x - 15$ 
B)  $x ^ { 3 } - 3 x ^ { 2 } + 5 x - 15$ 
C)  $x ^ { 3 } + 5 x ^ { 2 } - 3 x - 15$ 
D)  $x ^ { 2 } + 2 x - 15$

Question 2

Multiply.
-$( x - 6 ) ( 3 x - 6 )$

Accepted Answer

A)  $3 x ^ { 2 } + 36 x - 24$ 
B)  $3 x ^ { 2 } - 24 x - 24$ 
C)  $3 x ^ { 2 } - 26 x + 36$ 
D)  $3 x ^ { 2 } - 24 x + 36$ 
A)  $3 x ^ { 2 } + 36 x - 24$ 
B)  $3 x ^ { 2 } - 24 x - 24$ 
C)  $3 x ^ { 2 } - 26 x + 36$ 
D)  $3 x ^ { 2 } - 24 x + 36$

Question 3

Multiply.
-$( 5 x - 7 y ) ^ { 2 }$

Accepted Answer

A)  $25 x ^ { 2 } + 49 y ^ { 2 }$ 
B)  $5 x ^ { 2 } - 70 x y + 49 y ^ { 2 }$ 
C)  $5 x ^ { 2 } + 49 y ^ { 2 }$ 
D)  $25 x ^ { 2 } - 70 x y + 49 y ^ { 2 }$ 
A)  $25 x ^ { 2 } + 49 y ^ { 2 }$ 
B)  $5 x ^ { 2 } - 70 x y + 49 y ^ { 2 }$ 
C)  $5 x ^ { 2 } + 49 y ^ { 2 }$ 
D)  $25 x ^ { 2 } - 70 x y + 49 y ^ { 2 }$

Question 4

Write the number in standard notation.
-In the metric system of measurement, the prefix giga- means $1 \times 10 ^ { 9 }$. Write this number in standard notation.

Accepted Answer

A)  90 
B)  $0.000000001$ 
C)  $1,000,000,000$ 
D)  $100,000,000$ 
A)  90 
B)  $0.000000001$ 
C)  $1,000,000,000$ 
D)  $100,000,000$

Question 5

Write the number in standard notation.
-$6.0471 \times 10 ^ { - 7 }$

Accepted Answer

A)  $0.0000060471$ 
B)  $0.00000060471$ 
C)  $0.000000060471$ 
D)  $- 604710,000$ 
A)  $0.0000060471$ 
B)  $0.00000060471$ 
C)  $0.000000060471$ 
D)  $- 604710,000$

Question 6

Simplify the expression.
-$( 12 b ) ^ { 0 }$

Accepted Answer

A)  12 
B)  1 
C)  $b$ 
D)  0 
A)  12 
B)  1 
C)  $b$ 
D)  0

Question 7

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( \frac { 3 x ^ { 2 } y ^ { 4 } } { z ^ { 4 } } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 9 x ^ { 4 } y ^ { 8 } } { z ^ { 8 } }$ 
B)  $\frac { 3 x ^ { 4 } y ^ { 8 } } { z ^ { 8 } }$ 
C)  $\frac { 3 x ^ { 4 } y ^ { 8 } } { z ^ { 6 } }$ 
D)  $\frac { 9 x ^ { 4 } y ^ { 6 } } { z ^ { 6 } }$ 
A)  $\frac { 9 x ^ { 4 } y ^ { 8 } } { z ^ { 8 } }$ 
B)  $\frac { 3 x ^ { 4 } y ^ { 8 } } { z ^ { 8 } }$ 
C)  $\frac { 3 x ^ { 4 } y ^ { 8 } } { z ^ { 6 } }$ 
D)  $\frac { 9 x ^ { 4 } y ^ { 6 } } { z ^ { 6 } }$

Question 8

Perform the indicated operation.
-$( - 9 y + 7 ) + \left( - 2 y ^ { 2 } + 4 y - 2 \right)$

Accepted Answer

A)  $- 2 y ^ { 2 } + 5 y + 5$ 
B)  $- 2 y ^ { 2 } - 5 y + 5$ 
C)  $- 13 y ^ { 2 } - 2 y + 5$ 
D)  $- 2 y ^ { 2 } - 5 y + 9$ 
A)  $- 2 y ^ { 2 } + 5 y + 5$ 
B)  $- 2 y ^ { 2 } - 5 y + 5$ 
C)  $- 13 y ^ { 2 } - 2 y + 5$ 
D)  $- 2 y ^ { 2 } - 5 y + 9$

Question 9

Simplify the following by combining like terms.
-$6 x ^ { 8 } + 8 x ^ { 4 } + 2 x ^ { 8 }$

Accepted Answer

A)  $8 x ^ { 8 } + 8 x ^ { 4 }$ 
B)  $16 x ^ { 20 }$ 
C)  $16 x ^ { 4 }$ 
D)  cannot be simplified 
A)  $8 x ^ { 8 } + 8 x ^ { 4 }$ 
B)  $16 x ^ { 20 }$ 
C)  $16 x ^ { 4 }$ 
D)  cannot be simplified

Question 10

Fill in the blank with one of the words or phrases listed below.

-The of a term is its numerical factor.

Accepted Answer

A)  FOIL 
B)  coefficient 
C)  monomial 
D)  degree of a term 
A)  FOIL 
B)  coefficient 
C)  monomial 
D)  degree of a term

Question 11

Fill in the blank with one of the words or phrases listed below.

-A __________is a number or the product of numbers and variables raised to powers.

Accepted Answer

A)  coefficient 
B)  binomial 
C)  FOIL 
D)  term 
A)  coefficient 
B)  binomial 
C)  FOIL 
D)  term

Question 12

Simplify the expression.
-$\mathrm { d } ^ { 3 } \mathrm {~d} ^ { 2 } \mathrm {~d} ^ { 4 }$

Accepted Answer

A)  $24 \mathrm {~d} ^ { 3 }$ 
B)  $3 d ^ { 9 }$ 
C)  $\mathrm { d } ^ { 24 }$ 
D)  $\mathrm { d } ^ { 9 }$ 
A)  $24 \mathrm {~d} ^ { 3 }$ 
B)  $3 d ^ { 9 }$ 
C)  $\mathrm { d } ^ { 24 }$ 
D)  $\mathrm { d } ^ { 9 }$

Question 13

Find the perimeter.
-

Accepted Answer

A)  $2 x ^ { 2 } + 13 x + 9 m$ 
B)  $2 x ^ { 2 } - 5 x + 1 m$ 
C)  $2 x ^ { 2 } - 7 x + 1 m$ 
D)  $x ^ { 2 } - 7 x + 1 m$ 
A)  $2 x ^ { 2 } + 13 x + 9 m$ 
B)  $2 x ^ { 2 } - 5 x + 1 m$ 
C)  $2 x ^ { 2 } - 7 x + 1 m$ 
D)  $x ^ { 2 } - 7 x + 1 m$

Question 14

Simplify the expression. Write the result using positive exponents only.
-$( - 5 ) ^ { - 2 }$

Accepted Answer

A)  $\frac { 1 } { 25 }$ 
B)  $- \frac { 1 } { 25 }$ 
C)  25 
D)  $- 25$ 
A)  $\frac { 1 } { 25 }$ 
B)  $- \frac { 1 } { 25 }$ 
C)  25 
D)  $- 25$

Question 15

Multiply vertically.
-$\left( 5 x ^ { 2 } - 2 x + 5 \right) \left( x ^ { 2 } + 2 x + 2 \right)$

Accepted Answer

A)  $5 x ^ { 4 } + 10 x ^ { 3 } + 11 x ^ { 2 } + 6 x + 10$ 
B)  $5 x ^ { 4 } + 8 x ^ { 3 } + 6 x ^ { 2 } + 6 x + 10$ 
C)  $5 x ^ { 4 } + 10 x ^ { 3 } + 6 x ^ { 2 } + 6 x + 10$ 
D)  $5 x ^ { 4 } + 8 x ^ { 3 } + 11 x ^ { 2 } + 6 x + 10$ 
A)  $5 x ^ { 4 } + 10 x ^ { 3 } + 11 x ^ { 2 } + 6 x + 10$ 
B)  $5 x ^ { 4 } + 8 x ^ { 3 } + 6 x ^ { 2 } + 6 x + 10$ 
C)  $5 x ^ { 4 } + 10 x ^ { 3 } + 6 x ^ { 2 } + 6 x + 10$ 
D)  $5 x ^ { 4 } + 8 x ^ { 3 } + 11 x ^ { 2 } + 6 x + 10$

Question 16

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( - 9 x ^ { 3 } \right) ^ { 2 }$

Accepted Answer

A)  $81 x ^ { 5 }$ 
B)  $81 x ^ { 6 }$ 
C)  $- 9 x ^ { 6 }$ 
D)  $- 81 x ^ { 6 }$ 
A)  $81 x ^ { 5 }$ 
B)  $81 x ^ { 6 }$ 
C)  $- 9 x ^ { 6 }$ 
D)  $- 81 x ^ { 6 }$

Question 17

Perform the division.
-$\frac { 12 x ^ { 8 } - 8 x ^ { 5 } } { - 2 x ^ { 8 } }$

Accepted Answer

A)  $12 x ^ { 8 } + \frac { 4 } { x ^ { 3 } }$ 
B)  $- 6 - 8 x ^ { 5 }$ 
C)  $- 6 + 4 x ^ { 3 }$ 
D)  $- 6 + \frac { 4 } { x ^ { 3 } }$ 
A)  $12 x ^ { 8 } + \frac { 4 } { x ^ { 3 } }$ 
B)  $- 6 - 8 x ^ { 5 }$ 
C)  $- 6 + 4 x ^ { 3 }$ 
D)  $- 6 + \frac { 4 } { x ^ { 3 } }$

Question 18

Use the product rule to simplify the expression. Write the result using exponents.
-$( - 2 ) ^ { 2 } ( - 2 ) ^ { 7 }$

Accepted Answer

A)  $( - 2 ) ^ { 9 }$ 
B)   $(4) ^ { 9 }$ 
C)  $- 4 ^ { 14 }$ 
D)  $2 ^ { 9 }$ 
A)  $( - 2 ) ^ { 9 }$ 
B)   $(4) ^ { 9 }$ 
C)  $- 4 ^ { 14 }$ 
D)  $2 ^ { 9 }$

Question 19

Use synthetic division to divide.
-$\left( x ^ { 2 } - 49 \right) \div ( x - 7 )$

Accepted Answer

A)  $7 x + 7$ 
B)  $x + 7$ 
C)  $49 x + 7$ 
D)  $x + 49$ 
A)  $7 x + 7$ 
B)  $x + 7$ 
C)  $49 x + 7$ 
D)  $x + 49$

Question 20

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

Accepted Answer

A)  $\frac { y ^ { 3 } } { x ^ { - 4 } }$ 
B)  $\frac { x ^ { - 4 } } { y ^ { 3 } }$ 
C)  $\frac { 1 } { x ^ { 4 } y ^ { 10 } }$ 
D)  $\frac { x ^ { 4 } } { y ^ { 10 } }$ 
A)  $\frac { y ^ { 3 } } { x ^ { - 4 } }$ 
B)  $\frac { x ^ { - 4 } } { y ^ { 3 } }$ 
C)  $\frac { 1 } { x ^ { 4 } y ^ { 10 } }$ 
D)  $\frac { x ^ { 4 } } { y ^ { 10 } }$

Multiply using the FOIL method. - $( x + 5 ) \left( x ^ { 2 } - 3 \right)$

Multiply. - $( x - 6 ) ( 3 x - 6 )$

Multiply. - $( 5 x - 7 y ) ^ { 2 }$

Write the number in standard notation. -In the metric system of measurement, the prefix giga- means $1 \times 10 ^ { 9 }$ . Write this number in standard notation.

Write the number in standard notation. - $6.0471 \times 10 ^ { - 7 }$

Simplify the expression. - $( 12 b ) ^ { 0 }$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( \frac { 3 x ^ { 2 } y ^ { 4 } } { z ^ { 4 } } \right) ^ { 2 }$

Perform the indicated operation. - $( - 9 y + 7 ) + \left( - 2 y ^ { 2 } + 4 y - 2 \right)$

Simplify the following by combining like terms. - $6 x ^ { 8 } + 8 x ^ { 4 } + 2 x ^ { 8 }$

Fill in the blank with one of the words or phrases listed below. -The of a term is its numerical factor.

Fill in the blank with one of the words or phrases listed below. -A __________is a number or the product of numbers and variables raised to powers.

Simplify the expression. - $\mathrm { d } ^ { 3 } \mathrm {~d} ^ { 2 } \mathrm {~d} ^ { 4 }$

Find the perimeter. -

Simplify the expression. Write the result using positive exponents only. - $( - 5 ) ^ { - 2 }$

Multiply vertically. - $\left( 5 x ^ { 2 } - 2 x + 5 \right) \left( x ^ { 2 } + 2 x + 2 \right)$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( - 9 x ^ { 3 } \right) ^ { 2 }$

Perform the division. - $\frac { 12 x ^ { 8 } - 8 x ^ { 5 } } { - 2 x ^ { 8 } }$

Use the product rule to simplify the expression. Write the result using exponents. - $( - 2 ) ^ { 2 } ( - 2 ) ^ { 7 }$

Use synthetic division to divide. - $\left( x ^ { 2 } - 49 \right) \div ( x - 7 )$

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

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

Multiply using the FOIL method. - (x+5)(x2−3)( x + 5 ) \left( x ^ { 2 } - 3 \right)(x+5)(x2−3)

Multiply. - (x−6)(3x−6)( x - 6 ) ( 3 x - 6 )(x−6)(3x−6)

Multiply. - (5x−7y)2( 5 x - 7 y ) ^ { 2 }(5x−7y)2

Write the number in standard notation. -In the metric system of measurement, the prefix giga- means 1×1091 \times 10 ^ { 9 }1×109 . Write this number in standard notation.

Write the number in standard notation. - 6.0471×10−76.0471 \times 10 ^ { - 7 }6.0471×10−7

Simplify the expression. - (12b)0( 12 b ) ^ { 0 }(12b)0

Use the power rule and the power of a product or quotient rule to simplify the expression. - (3x2y4z4)2\left( \frac { 3 x ^ { 2 } y ^ { 4 } } { z ^ { 4 } } \right) ^ { 2 }(z43x2y4​)2

Perform the indicated operation. - (−9y+7)+(−2y2+4y−2)( - 9 y + 7 ) + \left( - 2 y ^ { 2 } + 4 y - 2 \right)(−9y+7)+(−2y2+4y−2)

Simplify the following by combining like terms. - 6x8+8x4+2x86 x ^ { 8 } + 8 x ^ { 4 } + 2 x ^ { 8 }6x8+8x4+2x8