Question 1

Simplify the radical expression. Assume all variables represent positive real numbers.
-$( \sqrt { 8 } + 3 ) ( \sqrt { 8 } - 3 )$

Accepted Answer

A)  $- 1$ 
B)  $8 - 2 \sqrt { 3 }$ 
C)  17 
D)  5 
A)  $- 1$ 
B)  $8 - 2 \sqrt { 3 }$ 
C)  17 
D)  5

Question 2

Completely factor the polynomial or state that the polynomial is prime.
-$15 ( x - 2 ) ^ { 2 } - 14 ( x - 2 ) - 49$

Accepted Answer

A)  $( 3 x + 13 ) ( 5 x + 17 )$ 
B)  $( 3 x + 9 ) ( 5 x + 9 )$ 
C)  $( 3 x + 7 ) ( 5 x + 7 )$ 
D)  $( 3 x - 13 ) ( 5 x - 3 )$ 
A)  $( 3 x + 13 ) ( 5 x + 17 )$ 
B)  $( 3 x + 9 ) ( 5 x + 9 )$ 
C)  $( 3 x + 7 ) ( 5 x + 7 )$ 
D)  $( 3 x - 13 ) ( 5 x - 3 )$

Question 3

Write the interval in set-builder notation and graph the set on a number line.
-$( - \infty , 5 )$

Accepted Answer

A)  $\{ x \mid x  5 \}$
  
A)  $\{ x \mid x  5 \}$

Question 4

Completely factor the polynomial or state that the polynomial is prime.
-$$15 z ^ { 2 } + 11 z - 12$$

Accepted Answer

A)  prime 
B)  $( 15 z + 4 ) ( z - 3 )$ 
C)  $( 3 z + 4 ) ( 5 z - 3 )$ 
D)  $( 3 z - 4 ) ( 5 z + 3 )$ 
A)  prime 
B)  $( 15 z + 4 ) ( z - 3 )$ 
C)  $( 3 z + 4 ) ( 5 z - 3 )$ 
D)  $( 3 z - 4 ) ( 5 z + 3 )$

Question 5

Simplify the rational expression.
-$$\frac { 9 x ^ { 2 } + 27 x ^ { 3 } } { 10 x + 30 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 9 x ^ { 2 } + 27 x ^ { 3 } } { 10 x + 30 x ^ { 2 } }$ 
B)  $\frac { 9 + 27 x ^ { 3 } } { 10 x + 30 }$ 
C)  $\frac { 9 } { 10 }$ 
D)  $\frac { 9 x } { 10 }$ 
A)  $\frac { 9 x ^ { 2 } + 27 x ^ { 3 } } { 10 x + 30 x ^ { 2 } }$ 
B)  $\frac { 9 + 27 x ^ { 3 } } { 10 x + 30 }$ 
C)  $\frac { 9 } { 10 }$ 
D)  $\frac { 9 x } { 10 }$

Question 6

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-$\left( 9 x 1 / 3 y ^ { 1 / 3 } \right) ^ { 2 }$

Accepted Answer

A)  $81 x ^ { 2 / 3 } y ^ { 2 / 3 }$ 
B)  $81 \mathrm { x } ^ { 1 / 6 } \mathrm { y } ^ { 1 / 6 }$ 
C)  $81 x ^ { 1 / 9 } y ^ { 1 / 9 }$ 
D)  $81 \mathrm { x } ^ { 2 } \mathrm { y } ^ { 2 }$ 
A)  $81 x ^ { 2 / 3 } y ^ { 2 / 3 }$ 
B)  $81 \mathrm { x } ^ { 1 / 6 } \mathrm { y } ^ { 1 / 6 }$ 
C)  $81 x ^ { 1 / 9 } y ^ { 1 / 9 }$ 
D)  $81 \mathrm { x } ^ { 2 } \mathrm { y } ^ { 2 }$

Question 7

Rationalize the denominator. Assume all variables represent positive real numbers.
-$\frac { 4 } { \sqrt { 7 } }$

Accepted Answer

A)  $\frac { 16 \sqrt { 7 } } { 7 }$ 
B)  $4 \sqrt { 7 }$ 
C)  $\frac { 4 \sqrt { 7 } } { 7 }$ 
D)  53 
A)  $\frac { 16 \sqrt { 7 } } { 7 }$ 
B)  $4 \sqrt { 7 }$ 
C)  $\frac { 4 \sqrt { 7 } } { 7 }$ 
D)  53

Question 8

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation.
-

Accepted Answer

A)  open infinite interval; $\{ x \mid x  - 6 \} ; ( - 6 , \infty )$ 
D)  closed infinite interval; $\{ x \mid x \leq - 6 \} ; ( - \infty , - 6 ]$ 
A)  open infinite interval; $\{ x \mid x  - 6 \} ; ( - 6 , \infty )$ 
D)  closed infinite interval; $\{ x \mid x \leq - 6 \} ; ( - \infty , - 6 ]$

Question 9

Add or subtract as indicated. Express the answer as a single polynomial in standard form.
-$$\left( 6 x ^ { 2 } + 7 x + 12 \right) - \left( 3 x ^ { 2 } - 6 x - 7 \right)$$

Accepted Answer

A)  $3 x ^ { 2 } + 10 x + 5$ 
B)  $3 x ^ { 2 } + 13 x + 19$ 
C)  $3 x ^ { 2 } + 13 x - 19$ 
D)  $3 x ^ { 2 } + 13 x + 5$ 
A)  $3 x ^ { 2 } + 10 x + 5$ 
B)  $3 x ^ { 2 } + 13 x + 19$ 
C)  $3 x ^ { 2 } + 13 x - 19$ 
D)  $3 x ^ { 2 } + 13 x + 5$

Question 10

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$- 3 y ^ { 0 }$

Accepted Answer

A)  $- 3$ 
B)  $- 2$ 
C)  0 
D)  1 
A)  $- 3$ 
B)  $- 2$ 
C)  0 
D)  1

Question 11

Use the associative property of multiplication to write an equivalent algebraic expression.
-6(3x)

Accepted Answer

A)  $( 6 \cdot 3 ) x$ 
B)  $( 6 \cdot 3 ) + x$ 
C)  $( 6 + 3 ) x$ 
D)  $6 ( 3 + x )$ 
A)  $( 6 \cdot 3 ) x$ 
B)  $( 6 \cdot 3 ) + x$ 
C)  $( 6 + 3 ) x$ 
D)  $6 ( 3 + x )$

Question 12

Factor out the greatest common factor.
-$21 x ^ { 4 } - 9 x ^ { 3 } + 15 x ^ { 2 }$

Accepted Answer

A)  $3 x ^ { 2 } \left( 7 x ^ { 2 } - 3 x + 5 \right)$ 
B)  $x ^ { 2 } \left( 21 x ^ { 2 } - 9 x + 15 \right)$ 
C)  $3 x \left( 7 x ^ { 3 } - 3 x ^ { 2 } + 5 x \right)$ 
D)  $3 \left( 7 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } \right)$ 
A)  $3 x ^ { 2 } \left( 7 x ^ { 2 } - 3 x + 5 \right)$ 
B)  $x ^ { 2 } \left( 21 x ^ { 2 } - 9 x + 15 \right)$ 
C)  $3 x \left( 7 x ^ { 3 } - 3 x ^ { 2 } + 5 x \right)$ 
D)  $3 \left( 7 x ^ { 4 } - 3 x ^ { 3 } + 5 x ^ { 2 } \right)$

Question 13

Completely factor the polynomial or state that the polynomial is prime.
-$$x ^ { 3 } - 216$$

Accepted Answer

A)  $( x - 6 ) \left( x ^ { 2 } + 6 x + 36 \right)$ 
B)  $( x - 6 ) \left( x ^ { 2 } + 36 \right)$ 
C)  $( x + 216 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x + 6 ) \left( x ^ { 2 } - 6 x + 36 \right)$ 
A)  $( x - 6 ) \left( x ^ { 2 } + 6 x + 36 \right)$ 
B)  $( x - 6 ) \left( x ^ { 2 } + 36 \right)$ 
C)  $( x + 216 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x + 6 ) \left( x ^ { 2 } - 6 x + 36 \right)$

Question 14

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 6 x } { - 48 x - 48 }$$

Accepted Answer

A)  $- \frac { x ^ { 2 } + 1 } { 8 }$ 
B)  $\frac { x + 1 } { 8 ( - x - 1 ) }$ 
C)  $- \frac { x ^ { 3 } + 1 } { 8 ( x + 1 ) }$ 
D)  $- \frac { 1 } { 8 }$ 
A)  $- \frac { x ^ { 2 } + 1 } { 8 }$ 
B)  $\frac { x + 1 } { 8 ( - x - 1 ) }$ 
C)  $- \frac { x ^ { 3 } + 1 } { 8 ( x + 1 ) }$ 
D)  $- \frac { 1 } { 8 }$

Question 15

Completely factor the polynomial or state that the polynomial is prime.
-$$81 x ^ { 2 } - 16$$

Accepted Answer

A)  $( 9 x + 4 ) ( 9 x - 4 )$ 
B)  $( 81 x + 1 ) ( x - 16 )$ 
C)  $( 9 x + 4 ) ^ { 2 }$ 
D)  $( 9 x - 4 ) ^ { 2 }$ 
A)  $( 9 x + 4 ) ( 9 x - 4 )$ 
B)  $( 81 x + 1 ) ( x - 16 )$ 
C)  $( 9 x + 4 ) ^ { 2 }$ 
D)  $( 9 x - 4 ) ^ { 2 }$

Question 16

Completely factor the polynomial or state that the polynomial is prime.
-$$( 11 - x ) ^ { 3 } - x ^ { 3 }$$

Accepted Answer

A)  $( 11 + 2 x ) \left( x ^ { 2 } - 11 x + 121 \right)$ 
B)  $( 11 - 2 x ) \left( 3 x ^ { 2 } - 11 x + 121 \right)$ 
C)  $( 11 - 2 x ) \left( x ^ { 2 } - 11 x + 121 \right)$ 
D)  $( 11 - x ) \left( x ^ { 2 } - 11 x + 121 \right)$ 
A)  $( 11 + 2 x ) \left( x ^ { 2 } - 11 x + 121 \right)$ 
B)  $( 11 - 2 x ) \left( 3 x ^ { 2 } - 11 x + 121 \right)$ 
C)  $( 11 - 2 x ) \left( x ^ { 2 } - 11 x + 121 \right)$ 
D)  $( 11 - x ) \left( x ^ { 2 } - 11 x + 121 \right)$

Question 17

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-$( - 27 ) ^ { 4 / 3 }$

Accepted Answer

A)  $- 81$ 
B)  not a real number 
C)  81 
D)  729 
A)  $- 81$ 
B)  not a real number 
C)  81 
D)  729

Question 18

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { 9 x ^ { 2 } - 64 } { x ^ { 2 } - 16 } \div \frac { 3 x + 8 } { x + 4 }$$

Accepted Answer

A)  $\frac { x - 4 } { 3 x - 8 }$ 
B)  $\frac { 3 x - 8 } { x - 4 }$ 
C)  $\frac { 3 x + 8 } { x + 4 }$ 
D)  $\frac { ( 3 x + 8 ) \left( 9 x ^ { 2 } - 64 \right) } { \left( x ^ { 2 } + 4 \right) ( x + 4 ) }$ 
A)  $\frac { x - 4 } { 3 x - 8 }$ 
B)  $\frac { 3 x - 8 } { x - 4 }$ 
C)  $\frac { 3 x + 8 } { x + 4 }$ 
D)  $\frac { ( 3 x + 8 ) \left( 9 x ^ { 2 } - 64 \right) } { \left( x ^ { 2 } + 4 \right) ( x + 4 ) }$

Question 19

Evaluate.
-$- 3 ^ { 3 }$

Accepted Answer

A)  27 
B)  9 
C)  $- 9$ 
D)  $- 27$ 
A)  27 
B)  9 
C)  $- 9$ 
D)  $- 27$

Question 20

Factor out the greatest common factor.
-$$x ( 6 x - 5 ) - 3 ( 6 x - 5 )$$

Accepted Answer

A)  $( 6 x - 5 ) ( x - 3 )$ 
B)  $( 6 x - 5 ) ( x + 3 )$ 
C)  $- 3 x ( 6 x - 5 )$ 
D)  $( 6 x - 3 ) ( x - 5 )$ 
A)  $( 6 x - 5 ) ( x - 3 )$ 
B)  $( 6 x - 5 ) ( x + 3 )$ 
C)  $- 3 x ( 6 x - 5 )$ 
D)  $( 6 x - 3 ) ( x - 5 )$

Simplify the radical expression. Assume all variables represent positive real numbers. - $( \sqrt { 8 } + 3 ) ( \sqrt { 8 } - 3 )$

Completely factor the polynomial or state that the polynomial is prime. - $15 ( x - 2 ) ^ { 2 } - 14 ( x - 2 ) - 49$

Write the interval in set-builder notation and graph the set on a number line. - $( - \infty , 5 )$ $Write the interval in set-builder notation and graph the set on a number line. - ( - \infty , 5 )$

Completely factor the polynomial or state that the polynomial is prime. - $15 z ^ { 2 } + 11 z - 12$

Simplify the rational expression. - $\frac { 9 x ^ { 2 } + 27 x ^ { 3 } } { 10 x + 30 x ^ { 2 } }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( 9 x 1 / 3 y ^ { 1 / 3 } \right) ^ { 2 }$

Rationalize the denominator. Assume all variables represent positive real numbers. - $\frac { 4 } { \sqrt { 7 } }$

Given the set sketched on the number line, identify the type of interval (open, closed, half-open, open infinite, closed infinite), write the set using set-builder notation, and write the set using interval notation. -

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 6 x ^ { 2 } + 7 x + 12 \right) - \left( 3 x ^ { 2 } - 6 x - 7 \right)$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $- 3 y ^ { 0 }$

Use the associative property of multiplication to write an equivalent algebraic expression. -6(3x)

Factor out the greatest common factor. - $21 x ^ { 4 } - 9 x ^ { 3 } + 15 x ^ { 2 }$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 3 } - 216$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 3 } + 1 } { x ^ { 3 } - x ^ { 2 } + x } \cdot \frac { 6 x } { - 48 x - 48 }$

Completely factor the polynomial or state that the polynomial is prime. - $81 x ^ { 2 } - 16$

Completely factor the polynomial or state that the polynomial is prime. - $( 11 - x ) ^ { 3 } - x ^ { 3 }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $( - 27 ) ^ { 4 / 3 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 9 x ^ { 2 } - 64 } { x ^ { 2 } - 16 } \div \frac { 3 x + 8 } { x + 4 }$

Evaluate. - $- 3 ^ { 3 }$

Factor out the greatest common factor. - $x ( 6 x - 5 ) - 3 ( 6 x - 5 )$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Filters

Exam 10: Math Exercises: Sets, Intervals, Absolute Value, and Properties

Simplify the radical expression. Assume all variables represent positive real numbers. - (8+3)(8−3)( \sqrt { 8 } + 3 ) ( \sqrt { 8 } - 3 )(8​+3)(8​−3)

Completely factor the polynomial or state that the polynomial is prime. - 15(x−2)2−14(x−2)−4915 ( x - 2 ) ^ { 2 } - 14 ( x - 2 ) - 4915(x−2)2−14(x−2)−49

Write the interval in set-builder notation and graph the set on a number line. - (−∞,5)( - \infty , 5 )(−∞,5)

Completely factor the polynomial or state that the polynomial is prime. - 15z2+11z−1215 z ^ { 2 } + 11 z - 1215z2+11z−12

Simplify the rational expression. - 9x2+27x310x+30x2\frac { 9 x ^ { 2 } + 27 x ^ { 3 } } { 10 x + 30 x ^ { 2 } }10x+30x29x2+27x3​

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - (9x1/3y1/3)2\left( 9 x 1 / 3 y ^ { 1 / 3 } \right) ^ { 2 }(9x1/3y1/3)2

Rationalize the denominator. Assume all variables represent positive real numbers. - 47\frac { 4 } { \sqrt { 7 } }7​4​