Question 1

Perform the division.
-$\frac { 49 x ^ { 7 } - 21 x ^ { 6 } + 56 x ^ { 5 } } { 7 x ^ { 6 } }$

Accepted Answer

A)  $7 x - 3$ 
B)  $7 x - 21 x ^ { 6 } + \frac { 8 } { x }$ 
C)  $7 x - 3 + \frac { 8 } { x }$ 
D)  $15 x - 3$ 
A)  $7 x - 3$ 
B)  $7 x - 21 x ^ { 6 } + \frac { 8 } { x }$ 
C)  $7 x - 3 + \frac { 8 } { x }$ 
D)  $15 x - 3$

Question 2

Solve.
-Find the area of the top of the table. Express the area as a product, then multiply and simplify.

Accepted Answer

A)  $\left( 100 x ^ { 2 } - 220 x - 121 \right) s q$ in. 
B)  $\left( x ^ { 2 } - 121 \right) s q i n$. 
C)  $\left( 100 x ^ { 2 } + 220 x - 121 \right) s q$ in. 
D)  $\left( 100 x ^ { 2 } - 121 \right) s q$ in. 
A)  $\left( 100 x ^ { 2 } - 220 x - 121 \right) s q$ in. 
B)  $\left( x ^ { 2 } - 121 \right) s q i n$. 
C)  $\left( 100 x ^ { 2 } + 220 x - 121 \right) s q$ in. 
D)  $\left( 100 x ^ { 2 } - 121 \right) s q$ in.

Question 3

Use synthetic division to divide.
-$\left( 4 x ^ { 2 } + 4 x - 24 \right) \div ( x + 3 )$

Accepted Answer

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

Question 4

Find the quotient using long division.
-$\frac { x ^ { 3 } + 125 } { x + 5 }$

Accepted Answer

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

Question 5

Write the number in scientific notation.
-$0.000009087$

Accepted Answer

A)  $9.087 \times 10 ^ { - 7 }$ 
B)  $9.087 \times 10 ^ { - 5 }$ 
C)  $9.087 \times 10 ^ { - 6 }$ 
D)  $9.087 \times 10 ^ { 6 }$ 
A)  $9.087 \times 10 ^ { - 7 }$ 
B)  $9.087 \times 10 ^ { - 5 }$ 
C)  $9.087 \times 10 ^ { - 6 }$ 
D)  $9.087 \times 10 ^ { 6 }$

Question 6

Multiply.
-$( a + 2 ) ( a + 5 )$

Accepted Answer

A)  $2 a + 10$ 
B)  $a ^ { 2 } + 7 a + 10$ 
C)  $2 a ^ { 2 } + 10$ 
D)  $a ^ { 2 } + 7 a + 7$ 
A)  $2 a + 10$ 
B)  $a ^ { 2 } + 7 a + 10$ 
C)  $2 a ^ { 2 } + 10$ 
D)  $a ^ { 2 } + 7 a + 7$

Question 7

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

-A polynomial with exactly 2 terms is called a .

Accepted Answer

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

Question 8

Multiply.
-$\left( x ^ { 2 } - 3 b \right) \left( x ^ { 2 } + 3 b \right)$

Accepted Answer

A)  $x ^ { 4 } - 6 x ^ { 2 } b + 9 b ^ { 2 }$ 
B)  $x ^ { 4 } + 6 x ^ { 2 } b + 9 b ^ { 2 }$ 
C)  $x ^ { 4 } - 9 b ^ { 2 }$ 
D)  $x ^ { 2 } - 9 b ^ { 2 }$ 
A)  $x ^ { 4 } - 6 x ^ { 2 } b + 9 b ^ { 2 }$ 
B)  $x ^ { 4 } + 6 x ^ { 2 } b + 9 b ^ { 2 }$ 
C)  $x ^ { 4 } - 9 b ^ { 2 }$ 
D)  $x ^ { 2 } - 9 b ^ { 2 }$

Question 9

Simplify the expression. Write the result using positive exponents only.
-$\frac { 10 r ^ { - 5 } \left( r ^ { 3 } \right) ^ { 3 } } { 3 \left( r ^ { 2 } \right) ^ { - 2 } }$

Accepted Answer

A)  $\frac { 10 r ^ { 8 } } { 3 }$ 
B)  $\frac { 10 } { 3 r ^ { 1 } }$ 
C)  $\frac { 10 r ^ { 1 } } { 3 }$ 
D)  $\frac { 10 } { 3 r ^ { 8 } }$ 
A)  $\frac { 10 r ^ { 8 } } { 3 }$ 
B)  $\frac { 10 } { 3 r ^ { 1 } }$ 
C)  $\frac { 10 r ^ { 1 } } { 3 }$ 
D)  $\frac { 10 } { 3 r ^ { 8 } }$

Question 10

Use synthetic division to divide.
-$\left( x ^ { 2 } - 14 x + 45 \right) \div ( x - 9 )$

Accepted Answer

A)  $x - 9$ 
B)  $x + 45$ 
C)  $x + 5$ 
D)  $x - 5$ 
A)  $x - 9$ 
B)  $x + 45$ 
C)  $x + 5$ 
D)  $x - 5$

Question 11

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

Accepted Answer

A)  $- 20 r ^ { 4 }$ 
B)  $- 20 r$ 
C)  $- 12 r - 8 r ^ { 4 }$ 
D)  cannot be simplified 
A)  $- 20 r ^ { 4 }$ 
B)  $- 20 r$ 
C)  $- 12 r - 8 r ^ { 4 }$ 
D)  cannot be simplified

Question 12

Perform the indicated operation.
-$( 26 x + 14 ) - \left( - 3 x ^ { 2 } - 13 x + 14 \right)$

Accepted Answer

A)  $- 3 x ^ { 2 } + 13 x + 28$ 
B)  $3 x ^ { 2 } - 39 x$ 
C)  $3 x ^ { 2 } + 39 x$ 
D)  $3 x ^ { 2 } + 39 x - 28$ 
A)  $- 3 x ^ { 2 } + 13 x + 28$ 
B)  $3 x ^ { 2 } - 39 x$ 
C)  $3 x ^ { 2 } + 39 x$ 
D)  $3 x ^ { 2 } + 39 x - 28$

Question 13

Evaluate the expression with the given replacement values.
-$x ^ { 5 } ; x = - 2$

Accepted Answer

A)  32 
B)  10 
C)  $- 32$ 
D)  $- 10$ 
A)  32 
B)  10 
C)  $- 32$ 
D)  $- 10$

Question 14

Perform the indicated operation.
-$\left( 3 x ^ { 2 } + 4 \right) + \left( 8 x ^ { 2 } + 20 \right)$

Accepted Answer

A)  $11 x ^ { 2 } + 16$ 
B)  $11 x ^ { 2 } + 24$ 
C)  $5 x ^ { 2 } + 16$ 
D)  $5 x ^ { 2 } + 24$ 
A)  $11 x ^ { 2 } + 16$ 
B)  $11 x ^ { 2 } + 24$ 
C)  $5 x ^ { 2 } + 16$ 
D)  $5 x ^ { 2 } + 24$

Question 15

Write the number in scientific notation.
-$0.000816$

Accepted Answer

A)  $8.16 \times 10 ^ { 4 }$ 
B)  $8.16 \times 10 ^ { - 5 }$ 
C)  $8.16 \times 10 ^ { - 3 }$ 
D)  $8.16 \times 10 ^ { - 4 }$ 
A)  $8.16 \times 10 ^ { 4 }$ 
B)  $8.16 \times 10 ^ { - 5 }$ 
C)  $8.16 \times 10 ^ { - 3 }$ 
D)  $8.16 \times 10 ^ { - 4 }$

Question 16

Solve.
-The cube has sides of length $2 y ^ { 5 }$ feet. Find its volume. $\left( V = s ^ { 3 } \right)$

Accepted Answer

A)  $6 \mathrm { y } ^ { 15 } \mathrm { cuft }$ 
B)  $6 \mathrm { y } ^ { 125 } \mathrm { cuft }$ 
C)  $8 \mathrm { y } ^ { 125 } \mathrm { cu } \mathrm { ft }$ 
D)  $8 \mathrm { y } 15 \mathrm { cu } \mathrm { ft }$ 
A)  $6 \mathrm { y } ^ { 15 } \mathrm { cuft }$ 
B)  $6 \mathrm { y } ^ { 125 } \mathrm { cuft }$ 
C)  $8 \mathrm { y } ^ { 125 } \mathrm { cu } \mathrm { ft }$ 
D)  $8 \mathrm { y } 15 \mathrm { cu } \mathrm { ft }$

Question 17

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$\left( x ^ { 7 } y \right) ^ { 3 }$

Accepted Answer

A)  $\mathrm { x } ^ { 10 } \mathrm { y } ^ { 4 }$ 
B)  $x ^ { 21 } y ^ { 3 }$ 
C)  $x ^ { 10 } y$ 
D)  $x ^ { 21 } y$ 
A)  $\mathrm { x } ^ { 10 } \mathrm { y } ^ { 4 }$ 
B)  $x ^ { 21 } y ^ { 3 }$ 
C)  $x ^ { 10 } y$ 
D)  $x ^ { 21 } y$

Question 18

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$P ( x ) = x ^ { 2 } + 9 x - 3 ; 3$

Accepted Answer

A)  15 
B)  36 
C)  27 
D)  33 
A)  15 
B)  36 
C)  27 
D)  33

Question 19

Multiply.
-$- 4 x ^ { 2 } \left( 7 x ^ { 2 } + 6 x - 6 \right)$

Accepted Answer

A)  $3 x ^ { 4 } + 2 x - 10$ 
B)  $- 28 x ^ { 4 } - 24 x + 24$ 
C)  $- 28 x ^ { 4 } - 24 x ^ { 2 } + 24$ 
D)  $- 28 x ^ { 4 } - 24 x ^ { 3 } + 24 x ^ { 2 }$ 
A)  $3 x ^ { 4 } + 2 x - 10$ 
B)  $- 28 x ^ { 4 } - 24 x + 24$ 
C)  $- 28 x ^ { 4 } - 24 x ^ { 2 } + 24$ 
D)  $- 28 x ^ { 4 } - 24 x ^ { 3 } + 24 x ^ { 2 }$

Question 20

Simplify the expression.
-$\frac { 3 a ^ { 9 } b ^ { 5 } c ^ { 10 } } { a b c }$

Accepted Answer

A)  $3 \mathrm { a } ^ { 10 } \mathrm {~b} _ { \mathrm { c } } 11$ 
B)  3a8b4c9 
C)  $\frac { a ^ { 8 } b ^ { 4 } c ^ { 9 } } { 2 }$ 
D)  $3 a ^ { 8 } b ^ { 4 } c ^ { 9 }$ 
A)  $3 \mathrm { a } ^ { 10 } \mathrm {~b} _ { \mathrm { c } } 11$ 
B)  3a8b4c9 
C)  $\frac { a ^ { 8 } b ^ { 4 } c ^ { 9 } } { 2 }$ 
D)  $3 a ^ { 8 } b ^ { 4 } c ^ { 9 }$

Perform the division. - $\frac { 49 x ^ { 7 } - 21 x ^ { 6 } + 56 x ^ { 5 } } { 7 x ^ { 6 } }$

Solve. -Find the area of the top of the table. Express the area as a product, then multiply and simplify.

Use synthetic division to divide. - $\left( 4 x ^ { 2 } + 4 x - 24 \right) \div ( x + 3 )$

Find the quotient using long division. - $\frac { x ^ { 3 } + 125 } { x + 5 }$

Write the number in scientific notation. - $0.000009087$

Multiply. - $( a + 2 ) ( a + 5 )$

Fill in the blank with one of the words or phrases listed below. -A polynomial with exactly 2 terms is called a .

Multiply. - $\left( x ^ { 2 } - 3 b \right) \left( x ^ { 2 } + 3 b \right)$

Simplify the expression. Write the result using positive exponents only. - $\frac { 10 r ^ { - 5 } \left( r ^ { 3 } \right) ^ { 3 } } { 3 \left( r ^ { 2 } \right) ^ { - 2 } }$

Use synthetic division to divide. - $\left( x ^ { 2 } - 14 x + 45 \right) \div ( x - 9 )$

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

Perform the indicated operation. - $( 26 x + 14 ) - \left( - 3 x ^ { 2 } - 13 x + 14 \right)$

Evaluate the expression with the given replacement values. - $x ^ { 5 } ; x = - 2$

Perform the indicated operation. - $\left( 3 x ^ { 2 } + 4 \right) + \left( 8 x ^ { 2 } + 20 \right)$

Write the number in scientific notation. - $0.000816$

Solve. -The cube has sides of length $2 y ^ { 5 }$ feet. Find its volume. $\left( V = s ^ { 3 } \right)$ $Solve. -The cube has sides of length 2 y ^ { 5 } feet. Find its volume. \left( V = s ^ { 3 } \right)$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $\left( x ^ { 7 } y \right) ^ { 3 }$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 2 } + 9 x - 3 ; 3$

Multiply. - $- 4 x ^ { 2 } \left( 7 x ^ { 2 } + 6 x - 6 \right)$

Simplify the expression. - $\frac { 3 a ^ { 9 } b ^ { 5 } c ^ { 10 } } { a b c }$

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

Perform the division. - 49x7−21x6+56x57x6\frac { 49 x ^ { 7 } - 21 x ^ { 6 } + 56 x ^ { 5 } } { 7 x ^ { 6 } }7x649x7−21x6+56x5​

Solve. -Find the area of the top of the table. Express the area as a product, then multiply and simplify.

Use synthetic division to divide. - (4x2+4x−24)÷(x+3)\left( 4 x ^ { 2 } + 4 x - 24 \right) \div ( x + 3 )(4x2+4x−24)÷(x+3)

Find the quotient using long division. - x3+125x+5\frac { x ^ { 3 } + 125 } { x + 5 }x+5x3+125​

Write the number in scientific notation. - 0.0000090870.0000090870.000009087

Multiply. - (a+2)(a+5)( a + 2 ) ( a + 5 )(a+2)(a+5)