Question 1

Factor out the greatest common factor.
-3x - 15

Accepted Answer

A)  $3 ( x - 15 )$ 
B)  $3 x ( - 5 )$ 
C)  $3 x ( x - 5 )$ 
D)  $3 ( x - 5 )$ 
A)  $3 ( x - 15 )$ 
B)  $3 x ( - 5 )$ 
C)  $3 x ( x - 5 )$ 
D)  $3 ( x - 5 )$

Question 2

Use the distributive property to multiply the given expressions.
-$$6 ( y - 2 x + 8 )$$

Accepted Answer

A)  $y - 12 x + 48$ 
B)  $6 y - 12 x + 8$ 
C)  $6 y - 12 x + 48$ 
D)  $6 y - 8 x + 14$ 
A)  $y - 12 x + 48$ 
B)  $6 y - 12 x + 8$ 
C)  $6 y - 12 x + 48$ 
D)  $6 y - 8 x + 14$

Question 3

Completely factor the polynomial or state that the polynomial is prime.
-$$x ^ { 2 } - 8 x + 16$$

Accepted Answer

A)  $( x - 4 ) ^ { 2 }$ 
B)  $( x - 8 ) ( x + 8 )$ 
C)  $( x + 4 ) ^ { 2 }$ 
D)  $( x - 4 ) ( x + 4 )$ 
A)  $( x - 4 ) ^ { 2 }$ 
B)  $( x - 8 ) ( x + 8 )$ 
C)  $( x + 4 ) ^ { 2 }$ 
D)  $( x - 4 ) ( x + 4 )$

Question 4

Perform the indicated operations. Express the answer as a single polynomial in standard form.
-$$( 6 y + 11 ) \left( 3 y ^ { 2 } - 2 y - 9 \right)$$

Accepted Answer

A)  $18 y ^ { 3 } + 21 y ^ { 2 } - 76 y - 99$ 
B)  $18 y ^ { 3 } - 12 y ^ { 2 } - 54 y + 11$ 
C)  $18 y ^ { 3 } + 45 y ^ { 2 } + 76 y + 99$ 
D)  $51 y ^ { 2 } - 34 y - 153$ 
A)  $18 y ^ { 3 } + 21 y ^ { 2 } - 76 y - 99$ 
B)  $18 y ^ { 3 } - 12 y ^ { 2 } - 54 y + 11$ 
C)  $18 y ^ { 3 } + 45 y ^ { 2 } + 76 y + 99$ 
D)  $51 y ^ { 2 } - 34 y - 153$

Question 5

List all the elements of B that belong to the given set.
-$$\mathrm { B } = \left\{ 8 , \sqrt { 8 } , - 22,0 , \frac { 5 } { 6 } , - \frac { 6 } { 5 } , 2.2,16 \pi , 0.168168168 \ldots \right\}$$
Integers

Accepted Answer

A)  $\{ 8 , - 22 \}$ 
B)  $\{ 8,0 \}$ 
C)  $\{ 8 , - 22,0 \}$ 
D)  $\{ 8,0 , \sqrt { 8 } \}$ 
A)  $\{ 8 , - 22 \}$ 
B)  $\{ 8,0 \}$ 
C)  $\{ 8 , - 22,0 \}$ 
D)  $\{ 8,0 , \sqrt { 8 } \}$

Question 6

Simplify the radical expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { 1000 }$

Accepted Answer

A)  32 
B)  10 
C)  100 
D)  $\pm 10$ 
A)  32 
B)  10 
C)  100 
D)  $\pm 10$

Question 7

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$4 ^ { - 3 } \cdot 4$

Accepted Answer

A)  16 
B)  $\frac { 1 } { 64 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  64 
A)  16 
B)  $\frac { 1 } { 64 }$ 
C)  $\frac { 1 } { 16 }$ 
D)  64

Question 8

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

Accepted Answer

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

Question 9

Evaluate the algebraic expression for the indicated variable.
-$$\frac { 7 x - 4 y } { x + 14 } \text { for } x = 8 , y = 5$$

Accepted Answer

A)  $\frac { 36 } { 19 }$ 
B)  $\frac { 18 } { 11 }$ 
C)  $\frac { 3 } { 22 }$ 
D)  $\frac { 3 } { 19 }$ 
A)  $\frac { 36 } { 19 }$ 
B)  $\frac { 18 } { 11 }$ 
C)  $\frac { 3 } { 22 }$ 
D)  $\frac { 3 } { 19 }$

Question 10

Simplify the radical expression. Assume all variables represent positive real numbers.
-$\sqrt [ 3 ] { - 27 }$

Accepted Answer

A)  5 
B)  $\pm 3$ 
C)  $- 3$ 
D)  9 
A)  5 
B)  $\pm 3$ 
C)  $- 3$ 
D)  9

Question 11

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$x ^ { - 8 } x ^ { 6 }$

Accepted Answer

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

Question 12

Evaluate the algebraic expression for the indicated variable.
-$- 4 x ^ { 2 } + 4 y ^ { 2 }$ for $x = 3 , y = - 2$

Accepted Answer

A)  $- 52$ 
B)  $- 20$ 
C)  4 
D)  $- 44$ 
A)  $- 52$ 
B)  $- 20$ 
C)  4 
D)  $- 44$

Question 13

Write the expression using exponential notation. Then identify the base and the exponent.
-$$x \cdot x \cdot x$$

Accepted Answer

A)  $4 ^ { X }$
base: $x$
exponent: 4 
B)  $4 ^ { x }$
base: 4
exponent: $x$ 
C)  $x ^ { 4 }$
base: 4
exponent: $x$ 
D)  $x ^ { 4 }$
base: $x$
exponent: 4 
A)  $4 ^ { X }$
base: $x$
exponent: 4 
B)  $4 ^ { x }$
base: 4
exponent: $x$ 
C)  $x ^ { 4 }$
base: 4
exponent: $x$ 
D)  $x ^ { 4 }$
base: $x$
exponent: 4

Question 14

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { \frac { x ^ { 2 } + 13 x + 40 } { x ^ { 2 } + 16 x + 64 } } { \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 17 x + 72 } }$$

Accepted Answer

A)  $x + 9$ 
B)  $\frac { x + 9 } { x ( x + 8 ) }$ 
C)  $\frac { x + 9 } { x }$ 
D)  $\frac { x } { ( x + 8 ) ( x + 8 ) }$ 
A)  $x + 9$ 
B)  $\frac { x + 9 } { x ( x + 8 ) }$ 
C)  $\frac { x + 9 } { x }$ 
D)  $\frac { x } { ( x + 8 ) ( x + 8 ) }$

Question 15

Evaluate the absolute value expression.
-$$| - 1 \cdot 3 + 7 \cdot 2 |$$

Accepted Answer

A)  11 
B)  13 
C)  17 
D)  1 
A)  11 
B)  13 
C)  17 
D)  1

Question 16

Completely factor the polynomial or state that the polynomial is prime.
-$128 x ^ { 2 } - 224 x + 98$

Accepted Answer

A)  $2 ( 8 x - 7 ) ^ { 2 }$ 
B)  prime 
C)  $2 ( 8 x + 7 ) ^ { 2 }$ 
D)  $2 ( 8 x - 7 ) ( 8 x + 7 )$ 
A)  $2 ( 8 x - 7 ) ^ { 2 }$ 
B)  prime 
C)  $2 ( 8 x + 7 ) ^ { 2 }$ 
D)  $2 ( 8 x - 7 ) ( 8 x + 7 )$

Question 17

Evaluate the algebraic expression for the indicated variable.
-$$\frac { 8 x y + 75 } { x } \text { for } x = 5 , y = 7$$

Accepted Answer

A) 23 
B) 15 
C) 131 
D) 71 
A) 23 
B) 15 
C) 131 
D) 71

Question 18

Completely factor the polynomial or state that the polynomial is prime.
-$$4 x ^ { 3 } + 12 x ^ { 2 } - 40 x$$

Accepted Answer

A)  $\left( 4 x ^ { 2 } + 8 x \right) ( x - 5 )$ 
B)  $( x - 2 ) \left( 4 x ^ { 2 } + 20 \right)$ 
C)  $4 x ( x + 2 ) ( x - 5 )$ 
D)  $4 x ( x - 2 ) ( x + 5 )$ 
A)  $\left( 4 x ^ { 2 } + 8 x \right) ( x - 5 )$ 
B)  $( x - 2 ) \left( 4 x ^ { 2 } + 20 \right)$ 
C)  $4 x ( x + 2 ) ( x - 5 )$ 
D)  $4 x ( x - 2 ) ( x + 5 )$

Factor out the greatest common factor. -3x - 15

Use the distributive property to multiply the given expressions. - $6 ( y - 2 x + 8 )$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 2 } - 8 x + 16$

Perform the indicated operations. Express the answer as a single polynomial in standard form. - $( 6 y + 11 ) \left( 3 y ^ { 2 } - 2 y - 9 \right)$

List all the elements of B that belong to the given set. - $\mathrm { B } = \left\{ 8 , \sqrt { 8 } , - 22,0 , \frac { 5 } { 6 } , - \frac { 6 } { 5 } , 2.2,16 \pi , 0.168168168 \ldots \right\}$ Integers

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { 1000 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $4 ^ { - 3 } \cdot 4$

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

Evaluate the algebraic expression for the indicated variable. - $\frac { 7 x - 4 y } { x + 14 } \text { for } x = 8 , y = 5$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { - 27 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $x ^ { - 8 } x ^ { 6 }$

Evaluate the algebraic expression for the indicated variable. - $- 4 x ^ { 2 } + 4 y ^ { 2 }$ for $x = 3 , y = - 2$

Write the expression using exponential notation. Then identify the base and the exponent. - $x \cdot x \cdot x$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { \frac { x ^ { 2 } + 13 x + 40 } { x ^ { 2 } + 16 x + 64 } } { \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 17 x + 72 } }$

Evaluate the absolute value expression. - $| - 1 \cdot 3 + 7 \cdot 2 |$

Completely factor the polynomial or state that the polynomial is prime. - $128 x ^ { 2 } - 224 x + 98$

Evaluate the algebraic expression for the indicated variable. - $\frac { 8 x y + 75 } { x } \text { for } x = 5 , y = 7$

Completely factor the polynomial or state that the polynomial is prime. - $4 x ^ { 3 } + 12 x ^ { 2 } - 40 x$

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

Factor out the greatest common factor. -3x - 15

Use the distributive property to multiply the given expressions. - 6(y−2x+8)6 ( y - 2 x + 8 )6(y−2x+8)

Completely factor the polynomial or state that the polynomial is prime. - x2−8x+16x ^ { 2 } - 8 x + 16x2−8x+16

Perform the indicated operations. Express the answer as a single polynomial in standard form. - (6y+11)(3y2−2y−9)( 6 y + 11 ) \left( 3 y ^ { 2 } - 2 y - 9 \right)(6y+11)(3y2−2y−9)

Simplify the radical expression. Assume all variables represent positive real numbers. - 10003\sqrt [ 3 ] { 1000 }31000​

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - 4−3⋅44 ^ { - 3 } \cdot 44−3⋅4

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 1−1x6+1x\frac { 1 - \frac { 1 } { x } } { 6 + \frac { 1 } { x } }6+x1​1−x1​​

Evaluate the algebraic expression for the indicated variable. - 7x−4yx+14 for x=8,y=5\frac { 7 x - 4 y } { x + 14 } \text { for } x = 8 , y = 5x+147x−4y​ for x=8,y=5

Simplify the radical expression. Assume all variables represent positive real numbers. - −273\sqrt [ 3 ] { - 27 }3−27​

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - x−8x6x ^ { - 8 } x ^ { 6 }x−8x6

Evaluate the algebraic expression for the indicated variable. - −4x2+4y2- 4 x ^ { 2 } + 4 y ^ { 2 }−4x2+4y2 for x=3,y=−2x = 3 , y = - 2x=3,y=−2

Write the expression using exponential notation. Then identify the base and the exponent. - x⋅x⋅xx \cdot x \cdot xx⋅x⋅x

Perform the indicated operations and simplify the result. Leave the answer in factored form. - x2+13x+40x2+16x+64x2+5xx2+17x+72\frac { \frac { x ^ { 2 } + 13 x + 40 } { x ^ { 2 } + 16 x + 64 } } { \frac { x ^ { 2 } + 5 x } { x ^ { 2 } + 17 x + 72 } }x2+17x+72x2+5x​x2+16x+64x2+13x+40​​

Evaluate the absolute value expression. - ∣−1⋅3+7⋅2∣| - 1 \cdot 3 + 7 \cdot 2 |∣−1⋅3+7⋅2∣

Completely factor the polynomial or state that the polynomial is prime. - 128x2−224x+98128 x ^ { 2 } - 224 x + 98128x2−224x+98

Evaluate the algebraic expression for the indicated variable. - 8xy+75x for x=5,y=7\frac { 8 x y + 75 } { x } \text { for } x = 5 , y = 7x8xy+75​ for x=5,y=7

Completely factor the polynomial or state that the polynomial is prime. - 4x3+12x2−40x4 x ^ { 3 } + 12 x ^ { 2 } - 40 x4x3+12x2−40x