Question 1

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

-The property is used to multiply 2x(x - 4).

Accepted Answer

A)  FOIL 
B)  binomial 
C)  distributive 
D)  monomial 
A)  FOIL 
B)  binomial 
C)  distributive 
D)  monomial

Question 2

Simplify the expression. Write the result using positive exponents only.
-$4 ^ { - 3 }$

Accepted Answer

A)  $\frac { 1 } { 12 }$ 
B)  64 
C)  $- 64$ 
D)  $\frac { 1 } { 64 }$ 
A)  $\frac { 1 } { 12 }$ 
B)  64 
C)  $- 64$ 
D)  $\frac { 1 } { 64 }$

Question 3

Simplify the expression. Write the result using positive exponents only.
-$\frac { x ^ { 3 } x ^ { 5 } } { x ^ { 4 } }$

Accepted Answer

A)  $x ^ { 11 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 12 }$ 
D)  $x ^ { 13 }$ 
A)  $x ^ { 11 }$ 
B)  $x ^ { 4 }$ 
C)  $x ^ { 12 }$ 
D)  $x ^ { 13 }$

Question 4

Multiply.
-$( 3 x + 0.5 ) ( 3 x - 0.5 )$

Accepted Answer

A)  $9 x ^ { 2 } - 2.5$ 
B)  $9 x ^ { 2 } - 1$ 
C)  $9 x ^ { 2 } - 0.25$ 
D)  $9 x ^ { 2 } - 3 x - 0.25$ 
A)  $9 x ^ { 2 } - 2.5$ 
B)  $9 x ^ { 2 } - 1$ 
C)  $9 x ^ { 2 } - 0.25$ 
D)  $9 x ^ { 2 } - 3 x - 0.25$

Question 5

Find the quotient using long division.
-$\frac { 5 r ^ { 3 } - 30 r ^ { 2 } - 26 r - 63 } { r - 7 }$

Accepted Answer

A)  $5 r ^ { 2 } - 5 r - 9$ 
B)  $5 r ^ { 2 } + 5 r + \frac { 9 } { r - 7 }$ 
C)  $r ^ { 2 } + 9 r + 5$ 
D)  $5 r ^ { 2 } + 5 r + 9$ 
A)  $5 r ^ { 2 } - 5 r - 9$ 
B)  $5 r ^ { 2 } + 5 r + \frac { 9 } { r - 7 }$ 
C)  $r ^ { 2 } + 9 r + 5$ 
D)  $5 r ^ { 2 } + 5 r + 9$

Question 6

Perform the indicated operation.
-$\left[ \left( 1.8 x ^ { 3 } + 7.1 x ^ { 2 } + 4.5 \right) + ( 6.6 x - 2.1 ) \right] - \left( 3.5 x ^ { 2 } - x - 9.8 \right)$

Accepted Answer

A)  $1.8 x ^ { 3 } + 3.6 x ^ { 2 } + 6.6 x + 12.2$ 
B)  $1.8 x ^ { 3 } + 3.6 x ^ { 2 } + 7.6 x + 12.2$ 
C)  $1.8 x ^ { 3 } + 10.6 x ^ { 2 } + 5.6 x - 7.4$ 
D)  $13 x ^ { 6 } + 12.2$ 
A)  $1.8 x ^ { 3 } + 3.6 x ^ { 2 } + 6.6 x + 12.2$ 
B)  $1.8 x ^ { 3 } + 3.6 x ^ { 2 } + 7.6 x + 12.2$ 
C)  $1.8 x ^ { 3 } + 10.6 x ^ { 2 } + 5.6 x - 7.4$ 
D)  $13 x ^ { 6 } + 12.2$

Question 7

Find the quotient using long division.
-$\frac { - 8 x ^ { 3 } - 6 x ^ { 2 } + 15 x + 11 } { 2 x + 3 }$

Accepted Answer

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

Question 8

Simplify the exponential expression. Write the result using only positive exponents.
-$\left( 3 x ^ { 7 } \right) \left( - 9 x ^ { 9 } \right)$

Accepted Answer

A)  $- 27 x^{ 16}$ 
B)  $- 27 x ^ { 63 }$ 
C)  $27 x ^ { 16 }$ 
D)  $27 x ^ { 63 }$ 
A)  $- 27 x^{ 16}$ 
B)  $- 27 x ^ { 63 }$ 
C)  $27 x ^ { 16 }$ 
D)  $27 x ^ { 63 }$

Question 9

Perform the division.
-$\frac { 2 x ^ { 3 } y ^ { 3 } + 8 x y - x ^ { 2 } y ^ { 2 } } { 2 x y }$

Accepted Answer

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

Question 10

Multiply.
-$( 4 x + 2 ) ^ { 3 }$

Accepted Answer

A)  $64 x ^ { 3 } + 96 x ^ { 2 } + 48 x + 8$ 
B)  $16 x ^ { 2 } + 16 x + 4$ 
C)  $64 x ^ { 3 } + 96 x ^ { 2 } + 96 x + 8$ 
D)  $16 x ^ { 6 } + 8 x ^ { 3 } + 64$ 
A)  $64 x ^ { 3 } + 96 x ^ { 2 } + 48 x + 8$ 
B)  $16 x ^ { 2 } + 16 x + 4$ 
C)  $64 x ^ { 3 } + 96 x ^ { 2 } + 96 x + 8$ 
D)  $16 x ^ { 6 } + 8 x ^ { 3 } + 64$

Question 11

Multiply.
-$\left( 2.9 x ^ { 5 } \right) \left( 3 x ^ { 8 } \right)$

Accepted Answer

A)  $0.87 x ^ { 13 }$ 
B)  $8.7 x ^ { 13 }$ 
C)  87 x 40 
D)  $8.7 x ^ { 40 }$ 
A)  $0.87 x ^ { 13 }$ 
B)  $8.7 x ^ { 13 }$ 
C)  87 x 40 
D)  $8.7 x ^ { 40 }$

Question 12

Use synthetic division to divide.
-$\left( x ^ { 2 } + 9 x + 12 \right) \div ( x + 6 )$

Accepted Answer

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

Question 13

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$P ( x ) = 36 x ^ { 4 } - 6 x ^ { 3 } + x ^ { 2 } - x - 36 ; \frac { 1 } { 6 }$

Accepted Answer

A)  $- 36$ 
B)  36 
C)  $- \frac { 1301 } { 36 }$ 
D)  $\frac { 1301 } { 36 }$ 
A)  $- 36$ 
B)  36 
C)  $- \frac { 1301 } { 36 }$ 
D)  $\frac { 1301 } { 36 }$

Question 14

Multiply.
-$\left( \frac { 1 } { 6 } x ^ { 9 } \right) \left( \frac { 1 } { 8 } x ^ { 5 } \right)$

Accepted Answer

A)  $- \frac { 1 } { 48 } x ^ { 45 }$ 
B)  $\frac { 1 } { 48 } \mathrm { x } ^ { 45 }$ 
C)  $- \frac { 1 } { 48 } x ^ { 14 }$ 
D)  $\frac { 1 } { 48 } x ^ { 14 }$ 
A)  $- \frac { 1 } { 48 } x ^ { 45 }$ 
B)  $\frac { 1 } { 48 } \mathrm { x } ^ { 45 }$ 
C)  $- \frac { 1 } { 48 } x ^ { 14 }$ 
D)  $\frac { 1 } { 48 } x ^ { 14 }$

Question 15

Multiply.
-$( 9 x - 10 ) ^ { 2 }$

Accepted Answer

A)  $81 x ^ { 2 } + 100$ 
B)  $9 x ^ { 2 } - 180 x + 100$ 
C)  $9 x ^ { 2 } + 100$ 
D)  $81 x ^ { 2 } - 180 x + 100$ 
A)  $81 x ^ { 2 } + 100$ 
B)  $9 x ^ { 2 } - 180 x + 100$ 
C)  $9 x ^ { 2 } + 100$ 
D)  $81 x ^ { 2 } - 180 x + 100$

Question 16

Find the quotient using long division.
-$\frac { x ^ { 4 } + 16 } { x - 2 }$

Accepted Answer

A)  $x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8 + \frac { 32 } { x - 2 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 32 } { x - 2 }$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 16 } { x - 2 }$ 
A)  $x ^ { 3 } - 2 x ^ { 2 } + 4 x - 8 + \frac { 32 } { x - 2 }$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 32 } { x - 2 }$ 
C)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8$ 
D)  $x ^ { 3 } + 2 x ^ { 2 } + 4 x + 8 + \frac { 16 } { x - 2 }$

Question 17

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

Accepted Answer

A)  $- 8 x ^ { 2 } y ^ { 2 }$ 
B)  $16 x ^ { 2 } y ^ { 2 }$ 
C)  $16 x y$ 
D)  $- 8 x y$ 
A)  $- 8 x ^ { 2 } y ^ { 2 }$ 
B)  $16 x ^ { 2 } y ^ { 2 }$ 
C)  $16 x y$ 
D)  $- 8 x y$

Question 18

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

-The ________method may be used when multiplying two binomials.

Accepted Answer

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

Question 19

Evaluate the expression using exponential rules. Write the result in standard notation.
-$\left( 4 \times 10 ^ { 5 } \right) \times \left( 2 \times 10 ^ { 2 } \right)$

Accepted Answer

A)  $8,000,000$ 
B)  $80,000,000$ 
C)  $8,000,000,000$ 
D)  $800,000,000$ 
A)  $8,000,000$ 
B)  $80,000,000$ 
C)  $8,000,000,000$ 
D)  $800,000,000$

Question 20

Write the number in scientific notation.
-$36,000,000$

Accepted Answer

A)  $3.6 \times 10 ^ { 8 }$ 
B)  $3.6 \times 10 ^ { - 8 }$ 
C)  $3.6 \times 10 ^ { 7 }$ 
D)  $3.6 \times 10 ^ { - 7 }$ 
A)  $3.6 \times 10 ^ { 8 }$ 
B)  $3.6 \times 10 ^ { - 8 }$ 
C)  $3.6 \times 10 ^ { 7 }$ 
D)  $3.6 \times 10 ^ { - 7 }$

Fill in the blank with one of the words or phrases listed below. -The property is used to multiply 2x(x - 4).

Simplify the expression. Write the result using positive exponents only. - $4 ^ { - 3 }$

Simplify the expression. Write the result using positive exponents only. - $\frac { x ^ { 3 } x ^ { 5 } } { x ^ { 4 } }$

Multiply. - $( 3 x + 0.5 ) ( 3 x - 0.5 )$

Find the quotient using long division. - $\frac { 5 r ^ { 3 } - 30 r ^ { 2 } - 26 r - 63 } { r - 7 }$

Perform the indicated operation. - $\left[ \left( 1.8 x ^ { 3 } + 7.1 x ^ { 2 } + 4.5 \right) + ( 6.6 x - 2.1 ) \right] - \left( 3.5 x ^ { 2 } - x - 9.8 \right)$

Find the quotient using long division. - $\frac { - 8 x ^ { 3 } - 6 x ^ { 2 } + 15 x + 11 } { 2 x + 3 }$

Simplify the exponential expression. Write the result using only positive exponents. - $\left( 3 x ^ { 7 } \right) \left( - 9 x ^ { 9 } \right)$

Perform the division. - $\frac { 2 x ^ { 3 } y ^ { 3 } + 8 x y - x ^ { 2 } y ^ { 2 } } { 2 x y }$

Multiply. - $( 4 x + 2 ) ^ { 3 }$

Multiply. - $\left( 2.9 x ^ { 5 } \right) \left( 3 x ^ { 8 } \right)$

Use synthetic division to divide. - $\left( x ^ { 2 } + 9 x + 12 \right) \div ( x + 6 )$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = 36 x ^ { 4 } - 6 x ^ { 3 } + x ^ { 2 } - x - 36 ; \frac { 1 } { 6 }$

Multiply. - $\left( \frac { 1 } { 6 } x ^ { 9 } \right) \left( \frac { 1 } { 8 } x ^ { 5 } \right)$

Multiply. - $( 9 x - 10 ) ^ { 2 }$

Find the quotient using long division. - $\frac { x ^ { 4 } + 16 } { x - 2 }$

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

Fill in the blank with one of the words or phrases listed below. -The ________method may be used when multiplying two binomials.

Evaluate the expression using exponential rules. Write the result in standard notation. - $\left( 4 \times 10 ^ { 5 } \right) \times \left( 2 \times 10 ^ { 2 } \right)$

Write the number in scientific notation. - $36,000,000$

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

Fill in the blank with one of the words or phrases listed below. -The property is used to multiply 2x(x - 4).

Simplify the expression. Write the result using positive exponents only. - 4−34 ^ { - 3 }4−3

Simplify the expression. Write the result using positive exponents only. - x3x5x4\frac { x ^ { 3 } x ^ { 5 } } { x ^ { 4 } }x4x3x5​

Multiply. - (3x+0.5)(3x−0.5)( 3 x + 0.5 ) ( 3 x - 0.5 )(3x+0.5)(3x−0.5)

Find the quotient using long division. - 5r3−30r2−26r−63r−7\frac { 5 r ^ { 3 } - 30 r ^ { 2 } - 26 r - 63 } { r - 7 }r−75r3−30r2−26r−63​

Perform the indicated operation. - [(1.8x3+7.1x2+4.5)+(6.6x−2.1)]−(3.5x2−x−9.8)\left[ \left( 1.8 x ^ { 3 } + 7.1 x ^ { 2 } + 4.5 \right) + ( 6.6 x - 2.1 ) \right] - \left( 3.5 x ^ { 2 } - x - 9.8 \right)[(1.8x3+7.1x2+4.5)+(6.6x−2.1)]−(3.5x2−x−9.8)

Find the quotient using long division. - −8x3−6x2+15x+112x+3\frac { - 8 x ^ { 3 } - 6 x ^ { 2 } + 15 x + 11 } { 2 x + 3 }2x+3−8x3−6x2+15x+11​

Simplify the exponential expression. Write the result using only positive exponents. - (3x7)(−9x9)\left( 3 x ^ { 7 } \right) \left( - 9 x ^ { 9 } \right)(3x7)(−9x9)

Perform the division. - 2x3y3+8xy−x2y22xy\frac { 2 x ^ { 3 } y ^ { 3 } + 8 x y - x ^ { 2 } y ^ { 2 } } { 2 x y }2xy2x3y3+8xy−x2y2​

Multiply. - (4x+2)3( 4 x + 2 ) ^ { 3 }(4x+2)3

Multiply. - (2.9x5)(3x8)\left( 2.9 x ^ { 5 } \right) \left( 3 x ^ { 8 } \right)(2.9x5)(3x8)

Use synthetic division to divide. - (x2+9x+12)÷(x+6)\left( x ^ { 2 } + 9 x + 12 \right) \div ( x + 6 )(x2+9x+12)÷(x+6)

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=36x4−6x3+x2−x−36;16P ( x ) = 36 x ^ { 4 } - 6 x ^ { 3 } + x ^ { 2 } - x - 36 ; \frac { 1 } { 6 }P(x)=36x4−6x3+x2−x−36;61​

Multiply. - (16x9)(18x5)\left( \frac { 1 } { 6 } x ^ { 9 } \right) \left( \frac { 1 } { 8 } x ^ { 5 } \right)(61​x9)(81​x5)

Multiply. - (9x−10)2( 9 x - 10 ) ^ { 2 }(9x−10)2

Find the quotient using long division. - x4+16x−2\frac { x ^ { 4 } + 16 } { x - 2 }x−2x4+16​

Use the power rule and the power of a product or quotient rule to simplify the expression. - (−4xy)2( - 4 x y ) ^ { 2 }(−4xy)2