Question 1

Find the area of the shaded rectangle.
-

Accepted Answer

A)  $\left( 18 x ^ { 2 } + 30 x + 100 \right) s q$ in. 
B)  $\left( 18 x ^ { 2 } + 30 x - 100 \right) s q$ in. 
C)  $\left( 18 x ^ { 2 } - 30 x - 100 \right)$ sq in. 
D)  $\left( 18 x ^ { 2 } + 90 x - 100 \right)$ sq in. 
A)  $\left( 18 x ^ { 2 } + 30 x + 100 \right) s q$ in. 
B)  $\left( 18 x ^ { 2 } + 30 x - 100 \right) s q$ in. 
C)  $\left( 18 x ^ { 2 } - 30 x - 100 \right)$ sq in. 
D)  $\left( 18 x ^ { 2 } + 90 x - 100 \right)$ sq in.

Question 2

Write the number in scientific notation.
-$67,000$

Accepted Answer

A)  $6.7 \times 10 ^ { 3 }$ 
B)  $6.7 \times 10 ^ { - 3 }$ 
C)  $6.7 \times 10 ^ { - 4 }$ 
D)  $6.7 \times 10 ^ { 4 }$ 
A)  $6.7 \times 10 ^ { 3 }$ 
B)  $6.7 \times 10 ^ { - 3 }$ 
C)  $6.7 \times 10 ^ { - 4 }$ 
D)  $6.7 \times 10 ^ { 4 }$

Question 3

Write the number in standard notation.
-$7.335 \times 10 ^ { - 6 }$

Accepted Answer

A)  $- 7,335,000$ 
B)  $0.000007335$ 
C)  $0.0000007335$ 
D)  $0.00007335$ 
A)  $- 7,335,000$ 
B)  $0.000007335$ 
C)  $0.0000007335$ 
D)  $0.00007335$

Question 4

Simplify the following by combining like terms.
-$3.8 x ^ { 3 } - 6.4 x + 11.7 + 1.7 x - x ^ { 3 } - 8.7$

Accepted Answer

A)  $1.1 \mathrm { x } ^ { 4 }$ 
B)  $3.8 x ^ { 3 } + 8.1 x + 20.4$ 
C)  $2.8 x ^ { 3 } - 4.7 x + 3$ 
D)  cannot be simplified 
A)  $1.1 \mathrm { x } ^ { 4 }$ 
B)  $3.8 x ^ { 3 } + 8.1 x + 20.4$ 
C)  $2.8 x ^ { 3 } - 4.7 x + 3$ 
D)  cannot be simplified

Question 5

Use synthetic division to divide.
-$\left( 4 x ^ { 3 } + 19 x ^ { 2 } + 27 x - 8 \right) \div \left( x - \frac { 1 } { 4 } \right)$

Accepted Answer

A)  $4 x ^ { 2 } + 18 x + \frac { 45 } { 2 } + \frac { \frac { 15 } { 2 } } { x - \frac { 1 } { 4 } }$ 
B)  $4 x ^ { 2 } + 20 x + 32$ 
C)  $4 x ^ { 2 } - 20 x + 32$ 
D)  $4 x ^ { 2 } + 20 x + 32 - \frac { 16 } { x - \frac { 1 } { 4 } }$ 
A)  $4 x ^ { 2 } + 18 x + \frac { 45 } { 2 } + \frac { \frac { 15 } { 2 } } { x - \frac { 1 } { 4 } }$ 
B)  $4 x ^ { 2 } + 20 x + 32$ 
C)  $4 x ^ { 2 } - 20 x + 32$ 
D)  $4 x ^ { 2 } + 20 x + 32 - \frac { 16 } { x - \frac { 1 } { 4 } }$

Question 6

Perform the division.
-$\frac { m ^ { 3 } n ^ { 3 } + m n ^ { 3 } } { m n }$

Accepted Answer

A)  $m ^ { 2 } n ^ { 2 } + n ^ { 3 }$ 
B)  $m ^ { 2 } n ^ { 2 } + n ^ { 2 }$ 
C)  $m ^ { 2 } n ^ { 2 } + m n ^ { 2 }$ 
D)  $m ^ { 4 } n ^ { 4 } + m ^ { 2 } n ^ { 4 }$ 
A)  $m ^ { 2 } n ^ { 2 } + n ^ { 3 }$ 
B)  $m ^ { 2 } n ^ { 2 } + n ^ { 2 }$ 
C)  $m ^ { 2 } n ^ { 2 } + m n ^ { 2 }$ 
D)  $m ^ { 4 } n ^ { 4 } + m ^ { 2 } n ^ { 4 }$

Question 7

Multiply.
-$\left( x - \frac { 2 } { 5 } \right) \left( x - \frac { 1 } { 7 } \right)$

Accepted Answer

A)  $x ^ { 2 } - \frac { 3 } { 7 } x - \frac { 3 } { 35 }$ 
B)  $x ^ { 2 } - \frac { 19 } { 35 } x + \frac { 2 } { 35 }$ 
C)  $x ^ { 2 } - \frac { 3 } { 7 } x + \frac { 2 } { 35 }$ 
D)  $x ^ { 2 } - \frac { 9 } { 35 } x + \frac { 2 } { 35 }$ 
A)  $x ^ { 2 } - \frac { 3 } { 7 } x - \frac { 3 } { 35 }$ 
B)  $x ^ { 2 } - \frac { 19 } { 35 } x + \frac { 2 } { 35 }$ 
C)  $x ^ { 2 } - \frac { 3 } { 7 } x + \frac { 2 } { 35 }$ 
D)  $x ^ { 2 } - \frac { 9 } { 35 } x + \frac { 2 } { 35 }$

Question 8

Simplify.
-If $Q ( x ) = 5 x ^ { 2 } - 7 x + 1$, find $Q \left( \frac { 1 } { 4 } \right)$

Accepted Answer

A)  $\frac { 1 } { 16 }$ 
B)  $- \frac { 1 } { 16 }$ 
C)  $\frac { 7 } { 16 }$ 
D)  $- \frac { 7 } { 16 }$ 
A)  $\frac { 1 } { 16 }$ 
B)  $- \frac { 1 } { 16 }$ 
C)  $\frac { 7 } { 16 }$ 
D)  $- \frac { 7 } { 16 }$

Question 9

Simplify the following by combining like terms.
-$\frac { 3 } { 4 } x ^ { 2 } - \frac { 2 } { 5 } x + \frac { 1 } { 2 } + \frac { 3 } { 5 } x ^ { 2 } - \frac { 4 } { 5 } x - \frac { 2 } { 3 }$

Accepted Answer

A)  $\frac { 9 } { 2 } x ^ { 2 } + \frac { 16 } { 5 } x - \frac { 10 } { 3 }$ 
B)  $\frac { 27 } { 20 } x ^ { 2 } - \frac { 6 } { 5 } x - \frac { 1 } { 6 }$ 
C)  $\frac { 27 } { 20 } x ^ { 4 } - \frac { 6 } { 5 } x ^ { 2 } - \frac { 1 } { 6 }$ 
D)  $\frac { 3 } { 20 } x ^ { 6 } - \frac { 1 } { 6 }$ 
A)  $\frac { 9 } { 2 } x ^ { 2 } + \frac { 16 } { 5 } x - \frac { 10 } { 3 }$ 
B)  $\frac { 27 } { 20 } x ^ { 2 } - \frac { 6 } { 5 } x - \frac { 1 } { 6 }$ 
C)  $\frac { 27 } { 20 } x ^ { 4 } - \frac { 6 } { 5 } x ^ { 2 } - \frac { 1 } { 6 }$ 
D)  $\frac { 3 } { 20 } x ^ { 6 } - \frac { 1 } { 6 }$

Question 10

Evaluate the expression with the given replacement values.
-$x ^ { 2 } ; x = - 9$

Accepted Answer

A)  81 
B)  $- 18$ 
C)  $- 81$ 
D)  18 
A)  81 
B)  $- 18$ 
C)  $- 81$ 
D)  18

Question 11

Use the power rule and the power of a product or quotient rule to simplify the expression.
-$( \mathrm { rs } ) ^ { 8 }$

Accepted Answer

A)  $r ^ { 9 } s ^ { 9 }$ 
B)  $8 \mathrm { rs }$ 
C)  $\mathrm { rs } ^ { 8 }$ 
D)  $\mathrm { r } ^ { 8 } \mathrm {~s} ^ { 8 }$ 
A)  $r ^ { 9 } s ^ { 9 }$ 
B)  $8 \mathrm { rs }$ 
C)  $\mathrm { rs } ^ { 8 }$ 
D)  $\mathrm { r } ^ { 8 } \mathrm {~s} ^ { 8 }$

Question 12

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

Accepted Answer

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

Question 13

Simplify the expression. Write the result using positive exponents only.
-$\left( \frac { x y ^ { 5 } } { x ^ { 4 } y } \right) ^ { - 2 }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 6 } y ^ { 11 } }$ 
B)  $\frac { x ^ { 6 } } { y ^ { 8 } }$ 
C)  $\frac { 1 } { x ^ { 10 } y ^ { 12 } }$ 
D)  $\frac { y ^ { 8 } } { x ^ { 6 } }$ 
A)  $\frac { 1 } { x ^ { 6 } y ^ { 11 } }$ 
B)  $\frac { x ^ { 6 } } { y ^ { 8 } }$ 
C)  $\frac { 1 } { x ^ { 10 } y ^ { 12 } }$ 
D)  $\frac { y ^ { 8 } } { x ^ { 6 } }$

Question 14

Solve.
-The perimeter of a rectangle is $\left( 4 x ^ { 2 } + 8 x + 18 \right)$ inches and its length is $\left( x ^ { 2 } + 3 x + 6 \right)$ inches. Find its width.

Accepted Answer

A)  $\left( \frac { 8 } { 3 } x + 7 \right)$ in. 
B)  $\left( x ^ { 2 } + x + 3 \right)$ in. 
C)  $\left( 2 x ^ { 2 } + 4 x + 9 \right)$ in. 
D)  $\left( 3 x ^ { 2 } + 5 x + 12 \right)$ in. 
A)  $\left( \frac { 8 } { 3 } x + 7 \right)$ in. 
B)  $\left( x ^ { 2 } + x + 3 \right)$ in. 
C)  $\left( 2 x ^ { 2 } + 4 x + 9 \right)$ in. 
D)  $\left( 3 x ^ { 2 } + 5 x + 12 \right)$ in.

Question 15

Perform the division.
-$\frac { 27 r ^ { 8 } - 45 r ^ { 5 } } { 9 r }$

Accepted Answer

A)  $27 r ^ { 7 } - 45 r ^ { 4 }$ 
B)  $3 r ^ { 7 } - 5 r ^ { 4 }$ 
C)  $3 r ^ { 8 } - 5 r ^ { 5 }$ 
D)  $3 r ^ { 9 } - 5 r ^ { 6 }$ 
A)  $27 r ^ { 7 } - 45 r ^ { 4 }$ 
B)  $3 r ^ { 7 } - 5 r ^ { 4 }$ 
C)  $3 r ^ { 8 } - 5 r ^ { 5 }$ 
D)  $3 r ^ { 9 } - 5 r ^ { 6 }$

Question 16

Multiply.
-$\left( x + \frac { 4 } { 9 } \right) \left( x - \frac { 4 } { 9 } \right)$

Accepted Answer

A)  $x ^ { 2 } + 16 x - 9$ 
B)  $x ^ { 2 } - \frac { 16 } { 81 }$ 
C)  $x ^ { 2 } - 16 x - 9$ 
D)  $x ^ { 2 } - 16$ 
A)  $x ^ { 2 } + 16 x - 9$ 
B)  $x ^ { 2 } - \frac { 16 } { 81 }$ 
C)  $x ^ { 2 } - 16 x - 9$ 
D)  $x ^ { 2 } - 16$

Question 17

Simplify the expression.
-$\left( - 4 z ^ { 2 } \right) \left( 7 z ^ { 3 } \right)$

Accepted Answer

A)  $- 28 z ^ { 5 }$ 
B)  $5488 \mathrm { z } ^ { 5 }$ 
C)  $28 z ^ { 6 }$ 
D)  $- 28 z ^ { 6 }$ 
A)  $- 28 z ^ { 5 }$ 
B)  $5488 \mathrm { z } ^ { 5 }$ 
C)  $28 z ^ { 6 }$ 
D)  $- 28 z ^ { 6 }$

Question 18

Simplify the exponential expression. Write the result using only positive exponents.
-$\frac { y ^ { 10 } } { y ^ { 8 } }$

Accepted Answer

A)  $\mathrm { y } ^ { 18 }$ 
B)  $\frac { 1 } { \mathrm { y } ^ { 2 } }$ 
C)  $y ^ { 12 }$ 
D)  $y ^ { 2 }$ 
A)  $\mathrm { y } ^ { 18 }$ 
B)  $\frac { 1 } { \mathrm { y } ^ { 2 } }$ 
C)  $y ^ { 12 }$ 
D)  $y ^ { 2 }$

Question 19

Simplify.
-If $\mathrm { P } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 6 \mathrm { x } - 4$, find $\mathrm { P } ( 2 )$

Accepted Answer

A)  $- 6$ 
B)  $- 8$ 
C)  $- 14$ 
D)  $- 12$ 
A)  $- 6$ 
B)  $- 8$ 
C)  $- 14$ 
D)  $- 12$

Question 20

Divide.
-$\left( x ^ { 2 } + 9 x + 20 \right) \div ( x + 4 )$

Accepted Answer

A)  $x ^ { 2 } + 5$ 
B)  $x - 16$ 
C)  $x ^ { 3 } - 16$ 
D)  $x + 5$ 
A)  $x ^ { 2 } + 5$ 
B)  $x - 16$ 
C)  $x ^ { 3 } - 16$ 
D)  $x + 5$

Find the area of the shaded rectangle. -

Write the number in scientific notation. - $67,000$

Write the number in standard notation. - $7.335 \times 10 ^ { - 6 }$

Simplify the following by combining like terms. - $3.8 x ^ { 3 } - 6.4 x + 11.7 + 1.7 x - x ^ { 3 } - 8.7$

Use synthetic division to divide. - $\left( 4 x ^ { 3 } + 19 x ^ { 2 } + 27 x - 8 \right) \div \left( x - \frac { 1 } { 4 } \right)$

Perform the division. - $\frac { m ^ { 3 } n ^ { 3 } + m n ^ { 3 } } { m n }$

Multiply. - $\left( x - \frac { 2 } { 5 } \right) \left( x - \frac { 1 } { 7 } \right)$

Simplify. -If $Q ( x ) = 5 x ^ { 2 } - 7 x + 1$ , find $Q \left( \frac { 1 } { 4 } \right)$

Simplify the following by combining like terms. - $\frac { 3 } { 4 } x ^ { 2 } - \frac { 2 } { 5 } x + \frac { 1 } { 2 } + \frac { 3 } { 5 } x ^ { 2 } - \frac { 4 } { 5 } x - \frac { 2 } { 3 }$

Evaluate the expression with the given replacement values. - $x ^ { 2 } ; x = - 9$

Use the power rule and the power of a product or quotient rule to simplify the expression. - $( \mathrm { rs } ) ^ { 8 }$

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

Simplify the expression. Write the result using positive exponents only. - $\left( \frac { x y ^ { 5 } } { x ^ { 4 } y } \right) ^ { - 2 }$

Perform the division. - $\frac { 27 r ^ { 8 } - 45 r ^ { 5 } } { 9 r }$

Multiply. - $\left( x + \frac { 4 } { 9 } \right) \left( x - \frac { 4 } { 9 } \right)$

Simplify the expression. - $\left( - 4 z ^ { 2 } \right) \left( 7 z ^ { 3 } \right)$

Simplify the exponential expression. Write the result using only positive exponents. - $\frac { y ^ { 10 } } { y ^ { 8 } }$

Simplify. -If $\mathrm { P } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 6 \mathrm { x } - 4$ , find $\mathrm { P } ( 2 )$

Divide. - $\left( x ^ { 2 } + 9 x + 20 \right) \div ( x + 4 )$

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

Find the area of the shaded rectangle. -

Write the number in scientific notation. - 67,00067,00067,000

Write the number in standard notation. - 7.335×10−67.335 \times 10 ^ { - 6 }7.335×10−6

Simplify the following by combining like terms. - 3.8x3−6.4x+11.7+1.7x−x3−8.73.8 x ^ { 3 } - 6.4 x + 11.7 + 1.7 x - x ^ { 3 } - 8.73.8x3−6.4x+11.7+1.7x−x3−8.7

Use synthetic division to divide. - (4x3+19x2+27x−8)÷(x−14)\left( 4 x ^ { 3 } + 19 x ^ { 2 } + 27 x - 8 \right) \div \left( x - \frac { 1 } { 4 } \right)(4x3+19x2+27x−8)÷(x−41​)

Perform the division. - m3n3+mn3mn\frac { m ^ { 3 } n ^ { 3 } + m n ^ { 3 } } { m n }mnm3n3+mn3​

Multiply. - (x−25)(x−17)\left( x - \frac { 2 } { 5 } \right) \left( x - \frac { 1 } { 7 } \right)(x−52​)(x−71​)

Simplify. -If Q(x)=5x2−7x+1Q ( x ) = 5 x ^ { 2 } - 7 x + 1Q(x)=5x2−7x+1 , find Q(14)Q \left( \frac { 1 } { 4 } \right)Q(41​)

Simplify the following by combining like terms. - 34x2−25x+12+35x2−45x−23\frac { 3 } { 4 } x ^ { 2 } - \frac { 2 } { 5 } x + \frac { 1 } { 2 } + \frac { 3 } { 5 } x ^ { 2 } - \frac { 4 } { 5 } x - \frac { 2 } { 3 }43​x2−52​x+21​+53​x2−54​x−32​

Evaluate the expression with the given replacement values. - x2;x=−9x ^ { 2 } ; x = - 9x2;x=−9

Use the power rule and the power of a product or quotient rule to simplify the expression. - (rs)8( \mathrm { rs } ) ^ { 8 }(rs)8

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

Simplify the expression. Write the result using positive exponents only. - (xy5x4y)−2\left( \frac { x y ^ { 5 } } { x ^ { 4 } y } \right) ^ { - 2 }(x4yxy5​)−2

Solve. -The perimeter of a rectangle is (4x2+8x+18)\left( 4 x ^ { 2 } + 8 x + 18 \right)(4x2+8x+18) inches and its length is (x2+3x+6)\left( x ^ { 2 } + 3 x + 6 \right)(x2+3x+6) inches. Find its width.

Perform the division. - 27r8−45r59r\frac { 27 r ^ { 8 } - 45 r ^ { 5 } } { 9 r }9r27r8−45r5​

Multiply. - (x+49)(x−49)\left( x + \frac { 4 } { 9 } \right) \left( x - \frac { 4 } { 9 } \right)(x+94​)(x−94​)

Simplify the expression. - (−4z2)(7z3)\left( - 4 z ^ { 2 } \right) \left( 7 z ^ { 3 } \right)(−4z2)(7z3)

Simplify the exponential expression. Write the result using only positive exponents. - y10y8\frac { y ^ { 10 } } { y ^ { 8 } }y8y10​

Simplify. -If P(x)=x2−6x−4\mathrm { P } ( \mathrm { x } ) = \mathrm { x } ^ { 2 } - 6 \mathrm { x } - 4P(x)=x2−6x−4 , find P(2)\mathrm { P } ( 2 )P(2)

Divide. - (x2+9x+20)÷(x+4)\left( x ^ { 2 } + 9 x + 20 \right) \div ( x + 4 )(x2+9x+20)÷(x+4)