Question 1

Completely factor the polynomial or state that the polynomial is prime.
-$343 y ^ { 3 } - 1$

Accepted Answer

A)  $( 343 y - 1 ) \left( y ^ { 2 } + 7 y + 1 \right)$ 
B)  $( 7 y + 1 ) \left( 49 y ^ { 2 } - 7 y + 1 \right)$ 
C)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 7 y + 1 \right)$ 
D)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 1 \right)$ 
A)  $( 343 y - 1 ) \left( y ^ { 2 } + 7 y + 1 \right)$ 
B)  $( 7 y + 1 ) \left( 49 y ^ { 2 } - 7 y + 1 \right)$ 
C)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 7 y + 1 \right)$ 
D)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 1 \right)$

Question 2

Simplify the expression using the order of operations.
-$$\frac { 6 + ( - 4 ) ^ { 2 } + 2 \cdot 2 ^ { 2 } } { 2 ^ { 2 } \cdot ( 5 - 3 ) }$$

Accepted Answer

A) 20 
B) 15 
C) 0 
D) 2 7 4 
A) 20 
B) 15 
C) 0 
D) 2 7 4

Question 3

Use the commutative property of addition to write an equivalent algebraic expression.
-5x + 8y

Accepted Answer

A) 8y + 5x 
B) 5x + 8y 
C) 5y + 8x 
D) 5x - 8y 
A) 8y + 5x 
B) 5x + 8y 
C) 5y + 8x 
D) 5x - 8y

Question 4

Evaluate the algebraic expression for the indicated variable.
-$- 7 a ^ { 2 } - 5 b + c - 13$ for $a = 8 , b = - 3 , c = - 5$

Accepted Answer

A)  $- 451$ 
B)  $- 455$ 
C)  $- 481$ 
D)  $- 59$ 
A)  $- 451$ 
B)  $- 455$ 
C)  $- 481$ 
D)  $- 59$

Question 5

Simplify the algebraic expression.
-$$4 ( 3 x - 4 ) - 8 ( x - 3 )$$

Accepted Answer

A)  $- 20 x + 8$ 
B)  $4 x - 40$ 
C)  $4 x + 8$ 
D)  $4 x - 7$ 
A)  $- 20 x + 8$ 
B)  $4 x - 40$ 
C)  $4 x + 8$ 
D)  $4 x - 7$

Question 6

Factor the polynomial by grouping.
-$12 x ^ { 2 } - 15 x - 16 x + 20$

Accepted Answer

A)  $( 12 x + 4 ) ( x + 5 )$ 
B)  $( 12 x - 4 ) ( x - 5 )$ 
C)  $( 3 x - 4 ) ( 4 x - 5 )$ 
D)  $( 3 x + 4 ) ( 4 x + 5 )$ 
A)  $( 12 x + 4 ) ( x + 5 )$ 
B)  $( 12 x - 4 ) ( x - 5 )$ 
C)  $( 3 x - 4 ) ( 4 x - 5 )$ 
D)  $( 3 x + 4 ) ( 4 x + 5 )$

Question 7

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { 8 x ^ { 2 } } { x - 1 } - \frac { 8 x } { x - 1 }$$

Accepted Answer

A)  $\frac { 8 x } { x - 1 }$ 
B)  0 
C)  $8 x$ 
D)  $\frac { 8 x ( x + 1 ) } { x - 1 }$ 
A)  $\frac { 8 x } { x - 1 }$ 
B)  0 
C)  $8 x$ 
D)  $\frac { 8 x ( x + 1 ) } { x - 1 }$

Question 8

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$$\left( - 3 x ^ { 4 } \right) \left( 6 x ^ { 5 } \right)$$

Accepted Answer

A)  $- 18 x ^ { 20 }$ 
B)  $18 x ^ { 20 }$ 
C)  $- 18 x ^ { 9 }$ 
D)  $18 x ^ { 9 }$ 
A)  $- 18 x ^ { 20 }$ 
B)  $18 x ^ { 20 }$ 
C)  $- 18 x ^ { 9 }$ 
D)  $18 x ^ { 9 }$

Question 9

Simplify the algebraic expression.
-$$- 15 x ^ { 3 } - 12 x ^ { 3 }$$

Accepted Answer

A)  $- 27 x ^ { 9 }$ 
B)  $- 27 x 6$ 
C)  $- 28 x ^ { 3 }$ 
D)  $- 27 x ^ { 3 }$ 
A)  $- 27 x ^ { 9 }$ 
B)  $- 27 x 6$ 
C)  $- 28 x ^ { 3 }$ 
D)  $- 27 x ^ { 3 }$

Question 10

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible.
-$2 c + 7 c$

Accepted Answer

A)  $9 \mathrm { c }$ 
B)  $- 5 c$ 
C)  $5 \mathrm { c }$ 
D)  $14 \mathrm { c }$ 
A)  $9 \mathrm { c }$ 
B)  $- 5 c$ 
C)  $5 \mathrm { c }$ 
D)  $14 \mathrm { c }$

Question 11

Evaluate.
-$5 ^ { 3 }$

Accepted Answer

A)  15 
B)  125 
C)  $- 15$ 
D)  $- 125$ 
A)  15 
B)  125 
C)  $- 15$ 
D)  $- 125$

Question 12

Simplify the algebraic expression.
-$$- 4 ( 2 x - 10 ) - 4 x + 5$$

Accepted Answer

A)  $4 x + 45$ 
B)  $12 x + 45$ 
C)  $- 12 x - 35$ 
D)  $- 12 x + 45$ 
A)  $4 x + 45$ 
B)  $12 x + 45$ 
C)  $- 12 x - 35$ 
D)  $- 12 x + 45$

Question 13

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { x ^ { 2 } + 12 x + 27 } { x ^ { 2 } + 16 x + 63 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 7 x + 12 }$$

Accepted Answer

A)  $\frac { 1 } { x + 4 }$ 
B)  $\frac { x } { x + 4 }$ 
C)  $\frac { x } { x ^ { 2 } + 16 x + 63 }$ 
D)  $\frac { x ^ { 2 } + 7 x } { x + 4 }$ 
A)  $\frac { 1 } { x + 4 }$ 
B)  $\frac { x } { x + 4 }$ 
C)  $\frac { x } { x ^ { 2 } + 16 x + 63 }$ 
D)  $\frac { x ^ { 2 } + 7 x } { x + 4 }$

Question 14

Completely factor the polynomial or state that the polynomial is prime.
-$3 x ^ { 2 } - 108$

Accepted Answer

A)  $3 ( x + 6 ) ( x - 6 )$ 
B)  $3 ( x - 6 ) ^ { 2 }$ 
C)  prime 
D)  $3 ( x + 6 ) ^ { 2 }$ 
A)  $3 ( x + 6 ) ( x - 6 )$ 
B)  $3 ( x - 6 ) ^ { 2 }$ 
C)  prime 
D)  $3 ( x + 6 ) ^ { 2 }$

Question 15

Completely factor the polynomial or state that the polynomial is prime.
-$10 x ^ { 2 } - 85 x + 175$

Accepted Answer

A)  $5 ( 2 x + 7 ) ( x + 5 )$ 
B)  $5 ( 2 x - 7 ) ( x - 5 )$ 
C)  $( 2 x - 7 ) ( 5 x - 5 )$ 
D)  prime 
A)  $5 ( 2 x + 7 ) ( x + 5 )$ 
B)  $5 ( 2 x - 7 ) ( x - 5 )$ 
C)  $( 2 x - 7 ) ( 5 x - 5 )$ 
D)  prime

Question 16

Perform the indicated operations and simplify the result. Leave the answer in factored form.
-$$\frac { 21 } { x - 9 } + \frac { 2 } { x - 9 }$$

Accepted Answer

A)  $\frac { 23 } { x - 9 }$ 
B)  $\frac { 19 } { x - 9 }$ 
C)  $\frac { 21 ( x - 9 ) } { 2 ( x - 9 ) }$ 
D)  $\frac { 19 } { x }$ 
A)  $\frac { 23 } { x - 9 }$ 
B)  $\frac { 19 } { x - 9 }$ 
C)  $\frac { 21 ( x - 9 ) } { 2 ( x - 9 ) }$ 
D)  $\frac { 19 } { x }$

Question 17

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

Accepted Answer

A)  $\frac { 1 } { x ^ { 9 } }$ 
B)  $- x ^ { 9 }$ 
C)  $\times ^ { 18 }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 18 } }$ 
A)  $\frac { 1 } { x ^ { 9 } }$ 
B)  $- x ^ { 9 }$ 
C)  $\times ^ { 18 }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 18 } }$

Question 18

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers.
-$\left( \frac { 1 } { 16 } \right) ^ { 1 / 4 }$

Accepted Answer

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

Question 19

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible.
-h $x - k x$

Accepted Answer

A)  $x ( h + k )$ 
B)  $x ( h - k )$ 
C)  $h ( x - k )$ 
D)  $( h - x ) k$ 
A)  $x ( h + k )$ 
B)  $x ( h - k )$ 
C)  $h ( x - k )$ 
D)  $( h - x ) k$

Question 20

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers.
-$$\left( - 3 x ^ { 5 } y ^ { - 6 } \right) \left( 5 x ^ { - 1 } y \right)$$

Accepted Answer

A)  $\frac { 2 x ^ { 4 } } { y ^ { 5 } }$ 
B)  $- 15 x ^ { 4 } y ^ { 7 }$ 
C)  $\frac { - 15 x ^ { 6 } } { y ^ { 7 } }$ 
D)  $\frac { - 15 x ^ { 4 } } { y ^ { 5 } }$ 
A)  $\frac { 2 x ^ { 4 } } { y ^ { 5 } }$ 
B)  $- 15 x ^ { 4 } y ^ { 7 }$ 
C)  $\frac { - 15 x ^ { 6 } } { y ^ { 7 } }$ 
D)  $\frac { - 15 x ^ { 4 } } { y ^ { 5 } }$

Completely factor the polynomial or state that the polynomial is prime. - $343 y ^ { 3 } - 1$

Simplify the expression using the order of operations. - $\frac { 6 + ( - 4 ) ^ { 2 } + 2 \cdot 2 ^ { 2 } } { 2 ^ { 2 } \cdot ( 5 - 3 ) }$

Use the commutative property of addition to write an equivalent algebraic expression. -5x + 8y

Evaluate the algebraic expression for the indicated variable. - $- 7 a ^ { 2 } - 5 b + c - 13$ for $a = 8 , b = - 3 , c = - 5$

Simplify the algebraic expression. - $4 ( 3 x - 4 ) - 8 ( x - 3 )$

Factor the polynomial by grouping. - $12 x ^ { 2 } - 15 x - 16 x + 20$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 8 x ^ { 2 } } { x - 1 } - \frac { 8 x } { x - 1 }$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\left( - 3 x ^ { 4 } \right) \left( 6 x ^ { 5 } \right)$

Simplify the algebraic expression. - $- 15 x ^ { 3 } - 12 x ^ { 3 }$

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible. - $2 c + 7 c$

Evaluate. - $5 ^ { 3 }$

Simplify the algebraic expression. - $- 4 ( 2 x - 10 ) - 4 x + 5$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { x ^ { 2 } + 12 x + 27 } { x ^ { 2 } + 16 x + 63 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 7 x + 12 }$

Completely factor the polynomial or state that the polynomial is prime. - $3 x ^ { 2 } - 108$

Completely factor the polynomial or state that the polynomial is prime. - $10 x ^ { 2 } - 85 x + 175$

Perform the indicated operations and simplify the result. Leave the answer in factored form. - $\frac { 21 } { x - 9 } + \frac { 2 } { x - 9 }$

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

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - $\left( \frac { 1 } { 16 } \right) ^ { 1 / 4 }$

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible. -h $x - k x$

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - $\left( - 3 x ^ { 5 } y ^ { - 6 } \right) \left( 5 x ^ { - 1 } y \right)$

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. - 343y3−1343 y ^ { 3 } - 1343y3−1

Simplify the expression using the order of operations. - 6+(−4)2+2⋅2222⋅(5−3)\frac { 6 + ( - 4 ) ^ { 2 } + 2 \cdot 2 ^ { 2 } } { 2 ^ { 2 } \cdot ( 5 - 3 ) }22⋅(5−3)6+(−4)2+2⋅22​

Use the commutative property of addition to write an equivalent algebraic expression. -5x + 8y

Evaluate the algebraic expression for the indicated variable. - −7a2−5b+c−13- 7 a ^ { 2 } - 5 b + c - 13−7a2−5b+c−13 for a=8,b=−3,c=−5a = 8 , b = - 3 , c = - 5a=8,b=−3,c=−5

Simplify the algebraic expression. - 4(3x−4)−8(x−3)4 ( 3 x - 4 ) - 8 ( x - 3 )4(3x−4)−8(x−3)

Factor the polynomial by grouping. - 12x2−15x−16x+2012 x ^ { 2 } - 15 x - 16 x + 2012x2−15x−16x+20

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 8x2x−1−8xx−1\frac { 8 x ^ { 2 } } { x - 1 } - \frac { 8 x } { x - 1 }x−18x2​−x−18x​

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - (−3x4)(6x5)\left( - 3 x ^ { 4 } \right) \left( 6 x ^ { 5 } \right)(−3x4)(6x5)

Simplify the algebraic expression. - −15x3−12x3- 15 x ^ { 3 } - 12 x ^ { 3 }−15x3−12x3

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible. - 2c+7c2 c + 7 c2c+7c

Evaluate. - 535 ^ { 3 }53

Simplify the algebraic expression. - −4(2x−10)−4x+5- 4 ( 2 x - 10 ) - 4 x + 5−4(2x−10)−4x+5

Perform the indicated operations and simplify the result. Leave the answer in factored form. - x2+12x+27x2+16x+63⋅x2+7xx2+7x+12\frac { x ^ { 2 } + 12 x + 27 } { x ^ { 2 } + 16 x + 63 } \cdot \frac { x ^ { 2 } + 7 x } { x ^ { 2 } + 7 x + 12 }x2+16x+63x2+12x+27​⋅x2+7x+12x2+7x​

Completely factor the polynomial or state that the polynomial is prime. - 3x2−1083 x ^ { 2 } - 1083x2−108

Completely factor the polynomial or state that the polynomial is prime. - 10x2−85x+17510 x ^ { 2 } - 85 x + 17510x2−85x+175

Perform the indicated operations and simplify the result. Leave the answer in factored form. - 21x−9+2x−9\frac { 21 } { x - 9 } + \frac { 2 } { x - 9 }x−921​+x−92​

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

Simplify the exponential expression. Write any negative exponents as positive exponents. Assume all variables represent positive real numbers. - (116)1/4\left( \frac { 1 } { 16 } \right) ^ { 1 / 4 }(161​)1/4

Use the distributive property to rewrite the sum or difference as a product. Simplify the answer if possible. -h x−kxx - k xx−kx

Use the laws of exponents to simplify each expression using positive exponents only. Assume all variables represent nonzero real numbers. - (−3x5y−6)(5x−1y)\left( - 3 x ^ { 5 } y ^ { - 6 } \right) \left( 5 x ^ { - 1 } y \right)(−3x5y−6)(5x−1y)