Question 1

Completely factor the polynomial or state that the polynomial is prime.
-$8 z ^ { 2 } - 6 z - 9$

Accepted Answer

A)  prime 
B)  $( 2 z - 3 ) ( 4 z + 3 )$ 
C)  $( 2 z + 3 ) ( 4 z - 3 )$ 
D)  $( 8 z - 3 ) ( z + 3 )$ 
A)  prime 
B)  $( 2 z - 3 ) ( 4 z + 3 )$ 
C)  $( 2 z + 3 ) ( 4 z - 3 )$ 
D)  $( 8 z - 3 ) ( z + 3 )$

Question 2

Simplify the rational expression.
-$$\frac { y ^ { 3 } - 216 } { y - 6 }$$

Accepted Answer

A)  $\frac { 1 } { \mathrm { y } - 6 }$ 
B)  $\frac { y ^ { 3 } - 216 } { y - 6 }$ 
C)  $y ^ { 2 } + 6 y + 36$ 
D)  $y ^ { 2 } - 36$ 
A)  $\frac { 1 } { \mathrm { y } - 6 }$ 
B)  $\frac { y ^ { 3 } - 216 } { y - 6 }$ 
C)  $y ^ { 2 } + 6 y + 36$ 
D)  $y ^ { 2 } - 36$

Question 3

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$$\left( \frac { - 6 x ^ { 6 } y ^ { 5 } } { 3 x ^ { 12 } y ^ { - 2 } } \right) ^ { 3 }$$

Accepted Answer

A)  $\frac { - 8 } { x ^ { 18 } y ^ { 21 } }$ 
B)  $\frac { - 8 y ^ { 21 } } { x ^ { 18 } }$ 
C)  $\frac { 8 y ^ { 21 } } { x ^ { 18 } }$ 
D)  $\frac { - 8 y ^ { 9 } } { x ^ { 18 } }$ 
A)  $\frac { - 8 } { x ^ { 18 } y ^ { 21 } }$ 
B)  $\frac { - 8 y ^ { 21 } } { x ^ { 18 } }$ 
C)  $\frac { 8 y ^ { 21 } } { x ^ { 18 } }$ 
D)  $\frac { - 8 y ^ { 9 } } { x ^ { 18 } }$

Question 4

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { \frac { 6 } { x } + 6 } { \frac { 6 } { x } - 6 }$$

Accepted Answer

A)  $\frac { x ^ { 2 } } { 6 - x ^ { 2 } }$ 
B)  $6 - x ^ { 2 }$ 
C)  $\frac { 6 ( 1 + x ) } { 1 - x }$ 
D)  $\frac { 1 + x } { 1 - x }$ 
A)  $\frac { x ^ { 2 } } { 6 - x ^ { 2 } }$ 
B)  $6 - x ^ { 2 }$ 
C)  $\frac { 6 ( 1 + x ) } { 1 - x }$ 
D)  $\frac { 1 + x } { 1 - x }$

Question 5

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible.
-$$6 a + 10 a$$

Accepted Answer

A)  $16 a$ 
B)  $- 4 a$ 
C)  $4 a$ 
D)  $30 a$ 
A)  $16 a$ 
B)  $- 4 a$ 
C)  $4 a$ 
D)  $30 a$

Question 6

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-64 1 / 3

Accepted Answer

A)  12 
B)  768 
C)  256 
D)  4 
A)  12 
B)  768 
C)  256 
D)  4

Question 7

Use the distributive property to multiply the given expressions.
-$$3 ( x - 3 )$$

Accepted Answer

A)  $3 x - 9$ 
B)  $3 x - 3$ 
C)  $3 x + 9$ 
D)  $x + 9$ 
A)  $3 x - 9$ 
B)  $3 x - 3$ 
C)  $3 x + 9$ 
D)  $x + 9$

Question 8

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { - 3 x + 7 } { x } + \frac { - 8 x - 2 } { 5 x }$$

Accepted Answer

A)  $\frac { - 23 x + 33 } { 5 x }$ 
B)  $\frac { - 23 x + 33 } { 5 x ^ { 2 } }$ 
C)  $\frac { - 23 x - 37 } { 5 x }$ 
D)  $\frac { - 7 x + 33 } { 5 x }$ 
A)  $\frac { - 23 x + 33 } { 5 x }$ 
B)  $\frac { - 23 x + 33 } { 5 x ^ { 2 } }$ 
C)  $\frac { - 23 x - 37 } { 5 x }$ 
D)  $\frac { - 7 x + 33 } { 5 x }$

Question 9

Find the quotient and the remainder.
-$x ^ { 2 } + 2 x - 39$ divided by $x + 8$

Accepted Answer

A)  $x - 6$; remainder 0 
B)  $x - 6$; remainder 9 
C)  $x + 6$; remainder 9 
D)  $x - 9$; remainder 6 
A)  $x - 6$; remainder 0 
B)  $x - 6$; remainder 9 
C)  $x + 6$; remainder 9 
D)  $x - 9$; remainder 6

Question 10

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { x + 4 } { x + 2 } - \frac { x + 4 } { x - 4 }$$

Accepted Answer

A)  $\frac { - 6 ( x + 4 ) } { ( x + 2 ) ( x - 4 ) }$ 
B)  $\frac { 6 ( x + 4 ) } { ( x + 2 ) ( x - 4 ) }$ 
C)  0 
D)  $\frac { - 2 ( x + 4 ) } { ( x + 2 ) ( x - 4 ) }$ 
A)  $\frac { - 6 ( x + 4 ) } { ( x + 2 ) ( x - 4 ) }$ 
B)  $\frac { 6 ( x + 4 ) } { ( x + 2 ) ( x - 4 ) }$ 
C)  0 
D)  $\frac { - 2 ( x + 4 ) } { ( x + 2 ) ( x - 4 ) }$

Question 11

Completely factor the polynomial or state that the polynomial is prime.
-$$\mathrm { x } ^ { 3 } + 125$$

Accepted Answer

A)  $( x - 5 ) \left( x ^ { 2 } + 5 x + 25 \right)$ 
B)  $( x + 5 ) \left( x ^ { 2 } + 25 \right)$ 
C)  $( x - 125 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x + 5 ) \left( x ^ { 2 } - 5 x + 25 \right)$ 
A)  $( x - 5 ) \left( x ^ { 2 } + 5 x + 25 \right)$ 
B)  $( x + 5 ) \left( x ^ { 2 } + 25 \right)$ 
C)  $( x - 125 ) \left( x ^ { 2 } - 1 \right)$ 
D)  $( x + 5 ) \left( x ^ { 2 } - 5 x + 25 \right)$

Question 12

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }$

Accepted Answer

A)  $\frac { x - 7 } { 49 }$ 
B)  $\frac { x + 7 } { 49 }$ 
C)  $\frac { 49 } { x + 7 }$ 
D)  $\frac { 49 } { x - 7 }$ 
A)  $\frac { x - 7 } { 49 }$ 
B)  $\frac { x + 7 } { 49 }$ 
C)  $\frac { 49 } { x + 7 }$ 
D)  $\frac { 49 } { x - 7 }$

Question 13

Completely factor the polynomial or state that the polynomial is prime.
-$9 x ^ { 2 } - 9 x - 54$

Accepted Answer

A)  $( 9 x + 18 ) ( x - 3 )$ 
B)  $9 ( x - 2 ) ( x + 3 )$ 
C)  prime 
D)  $9 ( x + 2 ) ( x - 3 )$ 
A)  $( 9 x + 18 ) ( x - 3 )$ 
B)  $9 ( x - 2 ) ( x + 3 )$ 
C)  prime 
D)  $9 ( x + 2 ) ( x - 3 )$

Question 14

Evaluate the absolute value expression.
-$$| - 5 + 6 |$$

Accepted Answer

A)  1 
B)  11 
C)  $- 11$ 
D)  $- 1$ 
A)  1 
B)  11 
C)  $- 11$ 
D)  $- 1$

Question 15

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$2 ^{- 4}$

Accepted Answer

A)  $- 16$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  16 
A)  $- 16$ 
B)  $\frac { 1 } { 8 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  16

Question 16

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { \frac { 3 } { x + 5 } + \frac { 9 } { x + 3 } } { \frac { 2 x + 9 } { x ^ { 2 } + 8 x + 15 } }$$

Accepted Answer

A)  $2 x + 9$ 
B)  $\frac { 1 } { 6 }$ 
C)  12 
D)  6 
A)  $2 x + 9$ 
B)  $\frac { 1 } { 6 }$ 
C)  12 
D)  6

Question 17

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-$$x ^ { - 2 / 5 } \cdot x ^ { 3 / 5 }$$

Accepted Answer

A)  $x ^ { - 1 / 5 }$ 
B)  $x ^ { 1 / 5 }$ 
C)  $x ^ { 6 / 5 }$ 
D)  $x ^ { 5 / 6 }$ 
A)  $x ^ { - 1 / 5 }$ 
B)  $x ^ { 1 / 5 }$ 
C)  $x ^ { 6 / 5 }$ 
D)  $x ^ { 5 / 6 }$

Question 18

Evaluate the absolute value expression.
-$$\frac { | 5 | } { 5 } + \frac { | - 2 | } { - 2 }$$

Accepted Answer

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

Question 19

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$\frac { x ^ { - 8 } } { x ^ { 3 } }$

Accepted Answer

A)  $\frac { 1 } { x ^ { 11 } }$ 
B)  $\frac { 1 } { x ^ { 24 } }$ 
C)  $x ^ { 11 }$ 
D)  $\frac { 1 } { x ^ { 5 } }$ 
A)  $\frac { 1 } { x ^ { 11 } }$ 
B)  $\frac { 1 } { x ^ { 24 } }$ 
C)  $x ^ { 11 }$ 
D)  $\frac { 1 } { x ^ { 5 } }$

Question 20

List all the elements of B that belong to the given set.
-$$B = \left\{ 18 , \sqrt { 6 } , - 22,0 , \frac { 3 } { 4 } , - \frac { 4 } { 3 } , 4.0 \right\}$$
Integers

Accepted Answer

A)  $\{ 18,0 , \sqrt { 6 } \}$ 
B)  $\{ 18 , - 22,0 \}$ 
C)  $\{ 18 , - 22 \}$ 
D)  $\{ 18,0 \}$ 
A)  $\{ 18,0 , \sqrt { 6 } \}$ 
B)  $\{ 18 , - 22,0 \}$ 
C)  $\{ 18 , - 22 \}$ 
D)  $\{ 18,0 \}$

Completely factor the polynomial or state that the polynomial is prime. - $8 z ^ { 2 } - 6 z - 9$

Simplify the rational expression. - $\frac { y ^ { 3 } - 216 } { y - 6 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\left( \frac { - 6 x ^ { 6 } y ^ { 5 } } { 3 x ^ { 12 } y ^ { - 2 } } \right) ^ { 3 }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 6 } { x } + 6 } { \frac { 6 } { x } - 6 }$

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible. - $6 a + 10 a$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. -64 ^{1 / 3}

Use the distributive property to multiply the given expressions. - $3 ( x - 3 )$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { - 3 x + 7 } { x } + \frac { - 8 x - 2 } { 5 x }$

Find the quotient and the remainder. - $x ^ { 2 } + 2 x - 39$ divided by $x + 8$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x + 4 } { x + 2 } - \frac { x + 4 } { x - 4 }$

Completely factor the polynomial or state that the polynomial is prime. - $\mathrm { x } ^ { 3 } + 125$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }$

Completely factor the polynomial or state that the polynomial is prime. - $9 x ^ { 2 } - 9 x - 54$

Evaluate the absolute value expression. - $| - 5 + 6 |$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $2 ^{- 4}$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { 3 } { x + 5 } + \frac { 9 } { x + 3 } } { \frac { 2 x + 9 } { x ^ { 2 } + 8 x + 15 } }$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $x ^ { - 2 / 5 } \cdot x ^ { 3 / 5 }$

Evaluate the absolute value expression. - $\frac { | 5 | } { 5 } + \frac { | - 2 | } { - 2 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\frac { x ^ { - 8 } } { x ^ { 3 } }$

List all the elements of B that belong to the given set. - $B = \left\{ 18 , \sqrt { 6 } , - 22,0 , \frac { 3 } { 4 } , - \frac { 4 } { 3 } , 4.0 \right\}$ Integers

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

Completely factor the polynomial or state that the polynomial is prime. - 8z2−6z−98 z ^ { 2 } - 6 z - 98z2−6z−9

Simplify the rational expression. - y3−216y−6\frac { y ^ { 3 } - 216 } { y - 6 }y−6y3−216​

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - (−6x6y53x12y−2)3\left( \frac { - 6 x ^ { 6 } y ^ { 5 } } { 3 x ^ { 12 } y ^ { - 2 } } \right) ^ { 3 }(3x12y−2−6x6y5​)3

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 6x+66x−6\frac { \frac { 6 } { x } + 6 } { \frac { 6 } { x } - 6 }x6​−6x6​+6​

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible. - 6a+10a6 a + 10 a6a+10a

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. -64 1 / 3

Use the distributive property to multiply the given expressions. - 3(x−3)3 ( x - 3 )3(x−3)

Perform the indicated operations and simplify the result. Leave the answer in factored form. - −3x+7x+−8x−25x\frac { - 3 x + 7 } { x } + \frac { - 8 x - 2 } { 5 x }x−3x+7​+5x−8x−2​

Find the quotient and the remainder. - x2+2x−39x ^ { 2 } + 2 x - 39x2+2x−39 divided by x+8x + 8x+8

Perform the indicated operations and simplify the result. Leave the answer in factored form. - x+4x+2−x+4x−4\frac { x + 4 } { x + 2 } - \frac { x + 4 } { x - 4 }x+2x+4​−x−4x+4​

Completely factor the polynomial or state that the polynomial is prime. - x3+125\mathrm { x } ^ { 3 } + 125x3+125

Perform the indicated operations and simplify the result. Leave the answer in factored form. - x49−1x1+7x\frac { \frac { x } { 49 } - \frac { 1 } { x } } { 1 + \frac { 7 } { x } }1+x7​49x​−x1​​

Completely factor the polynomial or state that the polynomial is prime. - 9x2−9x−549 x ^ { 2 } - 9 x - 549x2−9x−54

Evaluate the absolute value expression. - ∣−5+6∣| - 5 + 6 |∣−5+6∣

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - 2−42 ^{- 4}2−4

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 3x+5+9x+32x+9x2+8x+15\frac { \frac { 3 } { x + 5 } + \frac { 9 } { x + 3 } } { \frac { 2 x + 9 } { x ^ { 2 } + 8 x + 15 } }x2+8x+152x+9​x+53​+x+39​​

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - x−2/5⋅x3/5x ^ { - 2 / 5 } \cdot x ^ { 3 / 5 }x−2/5⋅x3/5

Evaluate the absolute value expression. - ∣5∣5+∣−2∣−2\frac { | 5 | } { 5 } + \frac { | - 2 | } { - 2 }5∣5∣​+−2∣−2∣​

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - x−8x3\frac { x ^ { - 8 } } { x ^ { 3 } }x3x−8​

List all the elements of B that belong to the given set. - B={18,6,−22,0,34,−43,4.0}B = \left\{ 18 , \sqrt { 6 } , - 22,0 , \frac { 3 } { 4 } , - \frac { 4 } { 3 } , 4.0 \right\}B={18,6​,−22,0,43​,−34​,4.0} Integers