Question 1

Rationalize the denominator. Assume all variables represent positive real numbers.
-$\frac { 2 } { 3 - \sqrt { 2 } }$

Accepted Answer

A)  $\frac { 6 + 2 \sqrt { 2 } } { - 1 }$ 
B)  $\frac { 2 } { 3 } - \frac { 2 } { \sqrt { 2 } }$ 
C)  $\frac { 6 - 2 \sqrt { 2 } } { 7 }$ 
D)  $\frac { 6 + 2 \sqrt { 2 } } { 7 }$ 
A)  $\frac { 6 + 2 \sqrt { 2 } } { - 1 }$ 
B)  $\frac { 2 } { 3 } - \frac { 2 } { \sqrt { 2 } }$ 
C)  $\frac { 6 - 2 \sqrt { 2 } } { 7 }$ 
D)  $\frac { 6 + 2 \sqrt { 2 } } { 7 }$

Question 2

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { 10 x ^ { 2 } - 3 x - 4 } { 5 x ^ { 2 } - x - 4 } \cdot \frac { 15 x ^ { 2 } + 12 x } { 1 - 4 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 3 x ( 5 x + 4 ) } { ( 1 - 2 x ) ( x - 1 ) }$ 
B)  $\frac { 3 x } { ( 1 - 2 x ) ( x - 1 ) }$ 
C) $\frac { ( 5 x + 4 ) ( 5 x - 4 ) } { ( 1 - 2 x ) ( x - 1 ) }$ 
D)  $\frac { 3 x ( 5 x - 4 ) } { ( 1 - 2 x ) ( x - 1 ) }$ 
A)  $\frac { 3 x ( 5 x + 4 ) } { ( 1 - 2 x ) ( x - 1 ) }$ 
B)  $\frac { 3 x } { ( 1 - 2 x ) ( x - 1 ) }$ 
C) $\frac { ( 5 x + 4 ) ( 5 x - 4 ) } { ( 1 - 2 x ) ( x - 1 ) }$ 
D)  $\frac { 3 x ( 5 x - 4 ) } { ( 1 - 2 x ) ( x - 1 ) }$

Question 3

Evaluate the absolute value expression.
-$4 | 4 | + 5 | - 9 |$

Accepted Answer

A)  29 
B)  61 
C)  $- 29$ 
D)  $- 61$ 
A)  29 
B)  61 
C)  $- 29$ 
D)  $- 61$

Question 4

Completely factor the polynomial or state that the polynomial is prime.
-$$( 4 x + 6 ) ^ { 3 } - 125$$

Accepted Answer

A)  $( 4 x + 1 ) \left( 16 x ^ { 2 } + 28 x + 31 \right)$ 
B)  $( 4 x + 1 ) \left( 16 x ^ { 2 } + 28 x + 91 \right)$ 
C)  $( 4 x + 1 ) \left( 16 x ^ { 2 } + 68 x + 91 \right)$ 
D)  $( 4 x + 11 ) \left( 16 x ^ { 2 } + 28 x + 31 \right)$ 
A)  $( 4 x + 1 ) \left( 16 x ^ { 2 } + 28 x + 31 \right)$ 
B)  $( 4 x + 1 ) \left( 16 x ^ { 2 } + 28 x + 91 \right)$ 
C)  $( 4 x + 1 ) \left( 16 x ^ { 2 } + 68 x + 91 \right)$ 
D)  $( 4 x + 11 ) \left( 16 x ^ { 2 } + 28 x + 31 \right)$

Question 5

Simplify the rational expression.
-$$\frac { 2 x ^ { 2 } - 16 x + 24 } { x - 6 }$$

Accepted Answer

A)  $\frac { 1 } { x - 6 }$ 
B)  $2 x - 4$ 
C)  $2 x ^ { 2 } - 20$ 
D)  $\frac { 2 x ^ { 2 } - 16 x + 24 } { x - 6 }$ 
A)  $\frac { 1 } { x - 6 }$ 
B)  $2 x - 4$ 
C)  $2 x ^ { 2 } - 20$ 
D)  $\frac { 2 x ^ { 2 } - 16 x + 24 } { x - 6 }$

Question 6

Simplify the expression using the order of operations.
-$$5 ^ { 2 } - 2 ( 3 ) + 24 \div 4$$

Accepted Answer

A) 25 
B) 33 
C) 43 
D) 7 4 
A) 25 
B) 33 
C) 43 
D) 7 4

Question 7

Simplify the radical expression. Assume all variables represent positive real numbers.
-$$\sqrt { \frac { 1 } { 16 } }$$

Accepted Answer

A)  16 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  $\frac { 1 } { 256 }$ 
A)  16 
B)  $\frac { 1 } { 4 }$ 
C)  4 
D)  $\frac { 1 } { 256 }$

Question 8

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

Accepted Answer

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

Question 9

Simplify the algebraic expression.
-$7 x + 2 x$

Accepted Answer

A)  $9 + x$ 
B)  $9 x$ 
C)  $5 x$ 
D)  $14 x$ 
A)  $9 + x$ 
B)  $9 x$ 
C)  $5 x$ 
D)  $14 x$

Question 10

Add or subtract as indicated. Express the answer as a single polynomial in standard form.
-$$\left( 4 x ^ { 7 } + 9 x ^ { 6 } - 6 x \right) + \left( 9 x ^ { 7 } + 8 x ^ { 6 } + 4 x \right)$$

Accepted Answer

A)  $13 x + 17 x ^ { 7 } - 2 x ^ { 6 }$ 
B)  $13 x ^ { 7 } + 17 x ^ { 6 } - 2 x$ 
C)  $3 x ^ { 7 } + 12 x ^ { 6 } + 13 x$ 
D)  $28 x ^ { 14 }$ 
A)  $13 x + 17 x ^ { 7 } - 2 x ^ { 6 }$ 
B)  $13 x ^ { 7 } + 17 x ^ { 6 } - 2 x$ 
C)  $3 x ^ { 7 } + 12 x ^ { 6 } + 13 x$ 
D)  $28 x ^ { 14 }$

Question 11

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-$\left( \frac { 1 } { 27 } \right) ^ { 2 / 3 }$

Accepted Answer

A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $- \frac { 1 } { 9 }$ 
D)  $\frac { 1 } { 13 }$ 
A)  $\frac { 1 } { 9 }$ 
B)  $\frac { 1 } { 4 }$ 
C)  $- \frac { 1 } { 9 }$ 
D)  $\frac { 1 } { 13 }$

Question 12

Simplify the expression using the order of operations.
-$$( - 2 - 7 ) \cdot ( - 2 + 6 ) - 5^3$$

Accepted Answer

A) 4 
B) -161 
C) 125 
D) 89 
A) 4 
B) -161 
C) 125 
D) 89

Question 13

Evaluate the absolute value expression.
-$$| 6 \cdot 8 - 7 \cdot 9 |$$

Accepted Answer

A)  15 
B)  111 
C)  $- 111$ 
D)  $- 15$ 
A)  15 
B)  111 
C)  $- 111$ 
D)  $- 15$

Question 14

Add or subtract as indicated. Express the answer as a single polynomial in standard form.
-$$\left( 3 x ^ { 6 } - 5 x ^ { 3 } - 13 \right) - \left( 8 x ^ { 6 } + 8 x ^ { 3 } + 18 \right)$$

Accepted Answer

A)  $- 49 x ^ { 9 }$ 
B)  $- 5 x ^ { 6 } - 13 x ^ { 3 } + 5$ 
C)  $- 5 x ^ { 6 } + 3 x ^ { 3 } + 5$ 
D)  $- 5 x ^ { 6 } - 13 x ^ { 3 } - 31$ 
A)  $- 49 x ^ { 9 }$ 
B)  $- 5 x ^ { 6 } - 13 x ^ { 3 } + 5$ 
C)  $- 5 x ^ { 6 } + 3 x ^ { 3 } + 5$ 
D)  $- 5 x ^ { 6 } - 13 x ^ { 3 } - 31$

Question 15

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$\frac { 8 } { 11 x } - \frac { 4 } { 11 x }$

Accepted Answer

A)  $\frac { 2 } { 11 x }$ 
B)  $\frac { 11 } { 4 x }$ 
C)  $\frac { 4 } { 11 x }$ 
D)  1 
A)  $\frac { 2 } { 11 x }$ 
B)  $\frac { 11 } { 4 x }$ 
C)  $\frac { 4 } { 11 x }$ 
D)  1

Question 16

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form.
-$( 5 x + 4 ) ^ { 3 }$

Accepted Answer

A)  $25 x ^ { 2 } + 40 x + 16$ 
B)  $125 x ^ { 3 } + 300 x ^ { 2 } + 240 x + 64$ 
C)  $125 x ^ { 3 } + 300 x ^ { 2 } + 300 x + 64$ 
D)  $25 x ^ { 6 } + 20 x ^ { 3 } + 4096$ 
A)  $25 x ^ { 2 } + 40 x + 16$ 
B)  $125 x ^ { 3 } + 300 x ^ { 2 } + 240 x + 64$ 
C)  $125 x ^ { 3 } + 300 x ^ { 2 } + 300 x + 64$ 
D)  $25 x ^ { 6 } + 20 x ^ { 3 } + 4096$

Question 17

Simplify the radical expression. Assume all variables represent positive real numbers.
-$\sqrt { 425 }$

Accepted Answer

A)  $25 \sqrt { 17 }$ 
B)  $5 \sqrt { 17 }$ 
C)  $\sqrt { 425 }$ 
D)  85 
A)  $25 \sqrt { 17 }$ 
B)  $5 \sqrt { 17 }$ 
C)  $\sqrt { 425 }$ 
D)  85

Question 18

Completely factor the polynomial or state that the polynomial is prime.
-$12 y ^ { 2 } + 17 y + 6$

Accepted Answer

A)  prime 
B)  $( 3 y + 2 ) ( 4 y + 3 )$ 
C)  $( 3 y - 2 ) ( 4 y - 3 )$ 
D)  $( 12 y + 2 ) ( y + 3 )$ 
A)  prime 
B)  $( 3 y + 2 ) ( 4 y + 3 )$ 
C)  $( 3 y - 2 ) ( 4 y - 3 )$ 
D)  $( 12 y + 2 ) ( y + 3 )$

Question 19

Completely factor the polynomial or state that the polynomial is prime.
-$$x ^ { 4 } + 4 x ^ { 2 } - 21$$

Accepted Answer

A)  $\left( x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 7 \right)$ 
B)  $\left( x ^ { 2 } - 3 \right) \left( x ^ { 2 } + 7 \right)$ 
C)  prime 
D)  $\left( x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 1 \right)$ 
A)  $\left( x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 7 \right)$ 
B)  $\left( x ^ { 2 } - 3 \right) \left( x ^ { 2 } + 7 \right)$ 
C)  prime 
D)  $\left( x ^ { 2 } + 3 \right) \left( x ^ { 2 } + 1 \right)$

Question 20

Completely factor the polynomial or state that the polynomial is prime.
-$27 x ^ { 3 } + 1$

Accepted Answer

A)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 3 x + 1 \right)$ 
B)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x + 1 \right)$ 
C)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x - 1 \right)$ 
D)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 1 \right)$ 
A)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 3 x + 1 \right)$ 
B)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x + 1 \right)$ 
C)  $( 3 x + 1 ) \left( 9 x ^ { 2 } - 3 x - 1 \right)$ 
D)  $( 3 x + 1 ) \left( 9 x ^ { 2 } + 1 \right)$

Rationalize the denominator. Assume all variables represent positive real numbers. - $\frac { 2 } { 3 - \sqrt { 2 } }$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 10 x ^ { 2 } - 3 x - 4 } { 5 x ^ { 2 } - x - 4 } \cdot \frac { 15 x ^ { 2 } + 12 x } { 1 - 4 x ^ { 2 } }$

Evaluate the absolute value expression. - $4 | 4 | + 5 | - 9 |$

Completely factor the polynomial or state that the polynomial is prime. - $( 4 x + 6 ) ^ { 3 } - 125$

Simplify the rational expression. - $\frac { 2 x ^ { 2 } - 16 x + 24 } { x - 6 }$

Simplify the expression using the order of operations. - $5 ^ { 2 } - 2 ( 3 ) + 24 \div 4$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 1 } { 16 } }$

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

Simplify the algebraic expression. - $7 x + 2 x$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 4 x ^ { 7 } + 9 x ^ { 6 } - 6 x \right) + \left( 9 x ^ { 7 } + 8 x ^ { 6 } + 4 x \right)$

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( \frac { 1 } { 27 } \right) ^ { 2 / 3 }$

Simplify the expression using the order of operations. - $( - 2 - 7 ) \cdot ( - 2 + 6 ) - 5^3$

Evaluate the absolute value expression. - $| 6 \cdot 8 - 7 \cdot 9 |$

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - $\left( 3 x ^ { 6 } - 5 x ^ { 3 } - 13 \right) - \left( 8 x ^ { 6 } + 8 x ^ { 3 } + 18 \right)$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 } { 11 x } - \frac { 4 } { 11 x }$

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - $( 5 x + 4 ) ^ { 3 }$

Simplify the radical expression. Assume all variables represent positive real numbers. - $\sqrt { 425 }$

Completely factor the polynomial or state that the polynomial is prime. - $12 y ^ { 2 } + 17 y + 6$

Completely factor the polynomial or state that the polynomial is prime. - $x ^ { 4 } + 4 x ^ { 2 } - 21$

Completely factor the polynomial or state that the polynomial is prime. - $27 x ^ { 3 } + 1$

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

Rationalize the denominator. Assume all variables represent positive real numbers. - 23−2\frac { 2 } { 3 - \sqrt { 2 } }3−2​2​

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 10x2−3x−45x2−x−4⋅15x2+12x1−4x2\frac { 10 x ^ { 2 } - 3 x - 4 } { 5 x ^ { 2 } - x - 4 } \cdot \frac { 15 x ^ { 2 } + 12 x } { 1 - 4 x ^ { 2 } }5x2−x−410x2−3x−4​⋅1−4x215x2+12x​

Evaluate the absolute value expression. - 4∣4∣+5∣−9∣4 | 4 | + 5 | - 9 |4∣4∣+5∣−9∣

Completely factor the polynomial or state that the polynomial is prime. - (4x+6)3−125( 4 x + 6 ) ^ { 3 } - 125(4x+6)3−125

Simplify the rational expression. - 2x2−16x+24x−6\frac { 2 x ^ { 2 } - 16 x + 24 } { x - 6 }x−62x2−16x+24​

Simplify the expression using the order of operations. - 52−2(3)+24÷45 ^ { 2 } - 2 ( 3 ) + 24 \div 452−2(3)+24÷4

Simplify the radical expression. Assume all variables represent positive real numbers. - 116\sqrt { \frac { 1 } { 16 } }161​​

Completely factor the polynomial or state that the polynomial is prime. - 49−x249 - x ^ { 2 }49−x2

Simplify the algebraic expression. - 7x+2x7 x + 2 x7x+2x

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - (4x7+9x6−6x)+(9x7+8x6+4x)\left( 4 x ^ { 7 } + 9 x ^ { 6 } - 6 x \right) + \left( 9 x ^ { 7 } + 8 x ^ { 6 } + 4 x \right)(4x7+9x6−6x)+(9x7+8x6+4x)

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - (127)2/3\left( \frac { 1 } { 27 } \right) ^ { 2 / 3 }(271​)2/3

Simplify the expression using the order of operations. - (−2−7)⋅(−2+6)−53( - 2 - 7 ) \cdot ( - 2 + 6 ) - 5^3(−2−7)⋅(−2+6)−53

Evaluate the absolute value expression. - ∣6⋅8−7⋅9∣| 6 \cdot 8 - 7 \cdot 9 |∣6⋅8−7⋅9∣

Add or subtract as indicated. Express the answer as a single polynomial in standard form. - (3x6−5x3−13)−(8x6+8x3+18)\left( 3 x ^ { 6 } - 5 x ^ { 3 } - 13 \right) - \left( 8 x ^ { 6 } + 8 x ^ { 3 } + 18 \right)(3x6−5x3−13)−(8x6+8x3+18)

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 811x−411x\frac { 8 } { 11 x } - \frac { 4 } { 11 x }11x8​−11x4​

Multiply the polynomials using a special product formula. Express the answer as a single polynomial in standard form. - (5x+4)3( 5 x + 4 ) ^ { 3 }(5x+4)3

Simplify the radical expression. Assume all variables represent positive real numbers. - 425\sqrt { 425 }425​

Completely factor the polynomial or state that the polynomial is prime. - 12y2+17y+612 y ^ { 2 } + 17 y + 612y2+17y+6

Completely factor the polynomial or state that the polynomial is prime. - x4+4x2−21x ^ { 4 } + 4 x ^ { 2 } - 21x4+4x2−21

Completely factor the polynomial or state that the polynomial is prime. - 27x3+127 x ^ { 3 } + 127x3+1