Question 1

Simplify. (Assume all variables are nonzero.)
-$\frac { 12 y ^ { 3 } } { 6 y }$

Accepted Answer

A)  $2 y$ 
B)  $2 y ^ { 2 }$ 
C)  $6 y ^ { 2 }$ 
D)  6 
A)  $2 y$ 
B)  $2 y ^ { 2 }$ 
C)  $6 y ^ { 2 }$ 
D)  6

Question 2

Solve the problem.
-The area of a square with side x is given by the function $$A ( x ) = x ^ { 2 }$$

Accepted Answer

A)  20 square feet 
B)  60 square feet 
C)  100 square feet 
D)  40 square feet 
A)  20 square feet 
B)  60 square feet 
C)  100 square feet 
D)  40 square feet

Question 3

Simplify. (Assume all variables are nonzero.)
-$15 ^ { 0 }$

Accepted Answer

A)  15 
B)  0 
C)  $- 1$ 
D)  1 
A)  15 
B)  0 
C)  $- 1$ 
D)  1

Question 4

Divide using long division.
-$$\left( x ^ { 2 } + 4 x + 4 \right) \div ( x + 2 )$$

Accepted Answer

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

Question 5

Perform the indicated calculation. Express your answer using scientific notation.
-$\left( 1.9 \times 10 ^ { - 7 } \right) \left( 1.6 \times 10 ^ { - 4 } \right)$

Accepted Answer

A)  $3.04 \times 10 ^ { 11 }$ 
B)  $3.04 \times 10 ^ { - 11 }$ 
C)  $3.5 \times 10 ^ { 11 }$ 
D)  $3.04 \times 10 ^ { 3 }$ 
A)  $3.04 \times 10 ^ { 11 }$ 
B)  $3.04 \times 10 ^ { - 11 }$ 
C)  $3.5 \times 10 ^ { 11 }$ 
D)  $3.04 \times 10 ^ { 3 }$

Question 6

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.)
-$$\frac { 4 x ^ { - 2 } } { y ^ { - 7 } z ^ { 5 } }$$

Accepted Answer

A)  $\frac { 4 } { x ^ { 2 } y ^ { 7 } z ^ { 5 } }$ 
B)  $\frac { 4 y ^ { 7 } } { x ^ { 2 } z ^ { 5 } }$ 
C)  $\frac { y ^ { 7 } } { 4 x ^ { 2 } z ^ { 5 } }$ 
D)  $\frac { 4 x ^ { 2 } } { y ^ { 7 } z ^ { 5 } }$ 
A)  $\frac { 4 } { x ^ { 2 } y ^ { 7 } z ^ { 5 } }$ 
B)  $\frac { 4 y ^ { 7 } } { x ^ { 2 } z ^ { 5 } }$ 
C)  $\frac { y ^ { 7 } } { 4 x ^ { 2 } z ^ { 5 } }$ 
D)  $\frac { 4 x ^ { 2 } } { y ^ { 7 } z ^ { 5 } }$

Question 7

Simplify. (Assume all variables are nonzero.)
-$$\frac { ( a - 3 b ) ^ { 15 } } { ( a - 3 b ) ^ { 5 } }$$

Accepted Answer

A)  $( a - 3 b ) ^ { 75 }$ 
B)  $( a - 3 b ) ^{10}$ 
C)  $( a - 3 b ) ^ { 3 }$ 
D)  $( a - 3 b ) ^ { 20 }$ 
A)  $( a - 3 b ) ^ { 75 }$ 
B)  $( a - 3 b ) ^{10}$ 
C)  $( a - 3 b ) ^ { 3 }$ 
D)  $( a - 3 b ) ^ { 20 }$

Question 8

Solve the problem. Round your answer to the nearest whole number, if necessary.
-Cindy determines that the revenue generated by candy sales for her high school can be approximated by the function $$R ( x ) = 5 x + 6$$

Accepted Answer

A)  $26 
B)  $14 
C)  $40 
D)  $11 
A)  $26 
B)  $14 
C)  $40 
D)  $11

Question 9

Find the special product using the appropriate formula.
-$$( x - 13 ) ^ { 2 }$$

Accepted Answer

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

Question 10

Find the special product using the appropriate formula.
-$$( 3 x + 8 ) ^ { 2 }$$

Accepted Answer

A)  $9 x ^ { 2 } + 64$ 
B)  $3 x ^ { 2 } + 64$ 
C)  $9 x ^ { 2 } + 48 x + 64$ 
D)  $3 x ^ { 2 } + 48 x + 64$ 
A)  $9 x ^ { 2 } + 64$ 
B)  $3 x ^ { 2 } + 64$ 
C)  $9 x ^ { 2 } + 48 x + 64$ 
D)  $3 x ^ { 2 } + 48 x + 64$

Question 11

Divide. Assume all variables are nonzero.
-$\frac { 6 x ^ { 8 } } { - 3 x ^ { 4 } }$

Accepted Answer

A)  $2 x ^ { 4 }$ 
B)  $- 2 x ^ { 4 }$ 
C)  $2 x ^{12}$ 
D)  $- 2 x^{12}$ 
A)  $2 x ^ { 4 }$ 
B)  $- 2 x ^ { 4 }$ 
C)  $2 x ^{12}$ 
D)  $- 2 x^{12}$

Question 12

Divide. Assume all variables are nonzero.
-$\frac { 36 x ^ { 10 } } { 21 x ^ { 5 } }$

Accepted Answer

A)  $5 x ^ { 5 }$ 
B)  $\frac { 24 } { 7 }$ 
C)  $\frac { 12 x ^ { 5 } } { 7 }$
$\text { 
D)  } \frac{12 x^{ 15}}{7}$ 
A)  $5 x ^ { 5 }$ 
B)  $\frac { 24 } { 7 }$ 
C)  $\frac { 12 x ^ { 5 } } { 7 }$
$\text { 
D)  } \frac{12 x^{ 15}}{7}$

Question 13

Divide. Assume all variables are nonzero.
-$$\left( 6 x ^ { 3 } + 12 x ^ { 2 } + 8 x \right) \div ( 2 x )$$

Accepted Answer

A)  25 
B)  $3 x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 }$ 
C)  $3 x ^ { 2 } + 6 x + 4$ 
D)  $3 x ^ { 2 } + 10 x$ 
A)  25 
B)  $3 x ^ { 4 } + 6 x ^ { 3 } + 4 x ^ { 2 }$ 
C)  $3 x ^ { 2 } + 6 x + 4$ 
D)  $3 x ^ { 2 } + 10 x$

Question 14

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero
real numbers.)
-$x ^ { 11 } \cdot x ^ { - 7 }$

Accepted Answer

A)  4 
B)  $x ^ { 4 }$ 
C)  $x ^ { 18 }$ 
D)  $\frac { x ^ { 11 } } { x ^ { 7 } }$ 
A)  4 
B)  $x ^ { 4 }$ 
C)  $x ^ { 18 }$ 
D)  $\frac { x ^ { 11 } } { x ^ { 7 } }$

Question 15

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

Accepted Answer

A)  $3 x ^ { 4 } + 3 x ^ { 3 } + 6 x ^ { 2 } - 20 x - 16$ 
B)  $3 x ^ { 4 } + 6 x ^ { 3 } + 6 x ^ { 2 } - 20 x - 16$ 
C)  $3 x ^ { 4 } + 6 x ^ { 3 } + 2 x ^ { 2 } - 20 x - 16$ 
D)  $3 x ^ { 4 } + 3 x ^ { 3 } + 2 x ^ { 2 } - 20 x - 16$ 
A)  $3 x ^ { 4 } + 3 x ^ { 3 } + 6 x ^ { 2 } - 20 x - 16$ 
B)  $3 x ^ { 4 } + 6 x ^ { 3 } + 6 x ^ { 2 } - 20 x - 16$ 
C)  $3 x ^ { 4 } + 6 x ^ { 3 } + 2 x ^ { 2 } - 20 x - 16$ 
D)  $3 x ^ { 4 } + 3 x ^ { 3 } + 2 x ^ { 2 } - 20 x - 16$

Question 16

Find the missing monomial, factor or term.
-$$7 x ^ { 5 } \cdot ? = 28 x ^ { 7 }$$

Accepted Answer

A)  $4 x ^ { 2 }$ 
B)  $- 4 x ^ { 2 }$ 
C)  $- x ^ { 2 }$ 
D)  $x ^ { 2 }$ 
A)  $4 x ^ { 2 }$ 
B)  $- 4 x ^ { 2 }$ 
C)  $- x ^ { 2 }$ 
D)  $x ^ { 2 }$

Question 17

Divide. Assume all variables are nonzero.
-$\frac { 48 x ^ { 10 } } { 6 x ^ { 8 } }$

Accepted Answer

A)  $42 x ^ { 2 }$ 
B)  $- 8 x ^ { 18 }$ 
C)  $8 x ^ { 2 }$ 
D)  $8 x ^ { 18 }$ 
A)  $42 x ^ { 2 }$ 
B)  $- 8 x ^ { 18 }$ 
C)  $8 x ^ { 2 }$ 
D)  $8 x ^ { 18 }$

Question 18

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the
polynomial.
-$$- x - 3 x ^ { 2 } - 4 x ^ { 3 } - 3 x ^ { 5 } + 4$$

Accepted Answer

A)  $- 3 x ^ { 5 } , - 3,5$ 
B)  $- x , - 1,1$ 
C)  $- 3 x ^ { 5 } , - 3,3$ 
D)  $3 x ^ { 5 } , 3,5$ 
A)  $- 3 x ^ { 5 } , - 3,5$ 
B)  $- x , - 1,1$ 
C)  $- 3 x ^ { 5 } , - 3,3$ 
D)  $3 x ^ { 5 } , 3,5$

Question 19

Multiply.
-$$( x - 7 ) ( x - 8 )$$

Accepted Answer

A)  $x ^ { 2 } + 56 x - 15$ 
B)  $x ^ { 2 } - 15 x - 15$ 
C)  $x ^ { 2 } - 15 x + 56$ 
D)  $x ^ { 2 } - 16 x + 56$ 
A)  $x ^ { 2 } + 56 x - 15$ 
B)  $x ^ { 2 } - 15 x - 15$ 
C)  $x ^ { 2 } - 15 x + 56$ 
D)  $x ^ { 2 } - 16 x + 56$

Question 20

Find the missing monomial, factor or term.
-$( x + ? ) ( x + ? ) = x ^ { 2 } + 9 x + 18$

Accepted Answer

A)  $- 3 , - 6$ 
B)  3,6 
C)  $- 3,6$ 
D)  $3 , - 6$ 
A)  $- 3 , - 6$ 
B)  3,6 
C)  $- 3,6$ 
D)  $3 , - 6$

Simplify. (Assume all variables are nonzero.) - $\frac { 12 y ^ { 3 } } { 6 y }$

Solve the problem. -The area of a square with side x is given by the function $A ( x ) = x ^ { 2 }$

Simplify. (Assume all variables are nonzero.) - $15 ^ { 0 }$

Divide using long division. - $\left( x ^ { 2 } + 4 x + 4 \right) \div ( x + 2 )$

Perform the indicated calculation. Express your answer using scientific notation. - $\left( 1.9 \times 10 ^ { - 7 } \right) \left( 1.6 \times 10 ^ { - 4 } \right)$

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - $\frac { 4 x ^ { - 2 } } { y ^ { - 7 } z ^ { 5 } }$

Simplify. (Assume all variables are nonzero.) - $\frac { ( a - 3 b ) ^ { 15 } } { ( a - 3 b ) ^ { 5 } }$

Solve the problem. Round your answer to the nearest whole number, if necessary. -Cindy determines that the revenue generated by candy sales for her high school can be approximated by the function $R ( x ) = 5 x + 6$

Find the special product using the appropriate formula. - $( x - 13 ) ^ { 2 }$

Find the special product using the appropriate formula. - $( 3 x + 8 ) ^ { 2 }$

Divide. Assume all variables are nonzero. - $\frac { 6 x ^ { 8 } } { - 3 x ^ { 4 } }$

Divide. Assume all variables are nonzero. - $\frac { 36 x ^ { 10 } } { 21 x ^ { 5 } }$

Divide. Assume all variables are nonzero. - $\left( 6 x ^ { 3 } + 12 x ^ { 2 } + 8 x \right) \div ( 2 x )$

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - $x ^ { 11 } \cdot x ^ { - 7 }$

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

Find the missing monomial, factor or term. - $7 x ^ { 5 } \cdot ? = 28 x ^ { 7 }$

Divide. Assume all variables are nonzero. - $\frac { 48 x ^ { 10 } } { 6 x ^ { 8 } }$

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - $- x - 3 x ^ { 2 } - 4 x ^ { 3 } - 3 x ^ { 5 } + 4$

Multiply. - $( x - 7 ) ( x - 8 )$

Find the missing monomial, factor or term. - $( x + ? ) ( x + ? ) = x ^ { 2 } + 9 x + 18$

Review of Real Numbers

Linear Equations

Graphing Linear Equations

Systems of Equations

Factoring and Quadratic Equations

Rational Expressions and Equations

A Transition

Radical Expressions and Equations

Quadratic Equations

Functions

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Simplify. (Assume all variables are nonzero.) - 12y36y\frac { 12 y ^ { 3 } } { 6 y }6y12y3​

Solve the problem. -The area of a square with side x is given by the function A(x)=x2A ( x ) = x ^ { 2 }A(x)=x2

Simplify. (Assume all variables are nonzero.) - 15015 ^ { 0 }150

Divide using long division. - (x2+4x+4)÷(x+2)\left( x ^ { 2 } + 4 x + 4 \right) \div ( x + 2 )(x2+4x+4)÷(x+2)

Perform the indicated calculation. Express your answer using scientific notation. - (1.9×10−7)(1.6×10−4)\left( 1.9 \times 10 ^ { - 7 } \right) \left( 1.6 \times 10 ^ { - 4 } \right)(1.9×10−7)(1.6×10−4)

Rewrite the expression without using negative exponents. (Assume all variables represent nonzero real numbers.) - 4x−2y−7z5\frac { 4 x ^ { - 2 } } { y ^ { - 7 } z ^ { 5 } }y−7z54x−2​

Simplify. (Assume all variables are nonzero.) - (a−3b)15(a−3b)5\frac { ( a - 3 b ) ^ { 15 } } { ( a - 3 b ) ^ { 5 } }(a−3b)5(a−3b)15​

Solve the problem. Round your answer to the nearest whole number, if necessary. -Cindy determines that the revenue generated by candy sales for her high school can be approximated by the function R(x)=5x+6R ( x ) = 5 x + 6R(x)=5x+6

Find the special product using the appropriate formula. - (x−13)2( x - 13 ) ^ { 2 }(x−13)2

Find the special product using the appropriate formula. - (3x+8)2( 3 x + 8 ) ^ { 2 }(3x+8)2

Divide. Assume all variables are nonzero. - 6x8−3x4\frac { 6 x ^ { 8 } } { - 3 x ^ { 4 } }−3x46x8​

Divide. Assume all variables are nonzero. - 36x1021x5\frac { 36 x ^ { 10 } } { 21 x ^ { 5 } }21x536x10​

Divide. Assume all variables are nonzero. - (6x3+12x2+8x)÷(2x)\left( 6 x ^ { 3 } + 12 x ^ { 2 } + 8 x \right) \div ( 2 x )(6x3+12x2+8x)÷(2x)

Simplify the expression. Write the result without using negative exponents. (Assume all variables represent nonzero real numbers.) - x11⋅x−7x ^ { 11 } \cdot x ^ { - 7 }x11⋅x−7

Multiply. - (3x2−3x−4)(x2+2x+4)\left( 3 x ^ { 2 } - 3 x - 4 \right) \left( x ^ { 2 } + 2 x + 4 \right)(3x2−3x−4)(x2+2x+4)

Find the missing monomial, factor or term. - 7x5⋅?=28x77 x ^ { 5 } \cdot ? = 28 x ^ { 7 }7x5⋅?=28x7

Divide. Assume all variables are nonzero. - 48x106x8\frac { 48 x ^ { 10 } } { 6 x ^ { 8 } }6x848x10​

Rewrite the polynomial in descending order. Identify the leading term, the leading coefficient, and the degree of the polynomial. - −x−3x2−4x3−3x5+4- x - 3 x ^ { 2 } - 4 x ^ { 3 } - 3 x ^ { 5 } + 4−x−3x2−4x3−3x5+4

Multiply. - (x−7)(x−8)( x - 7 ) ( x - 8 )(x−7)(x−8)

Find the missing monomial, factor or term. - (x+?)(x+?)=x2+9x+18( x + ? ) ( x + ? ) = x ^ { 2 } + 9 x + 18(x+?)(x+?)=x2+9x+18