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)  $( 7 y - 1 ) \left( 49 y ^ { 2 } + 1 \right)$

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

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

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)  $- 59$

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)  $4 x - 7$

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)  $( 3 x + 4 ) ( 4 x + 5 )$

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)  $\frac { 8 x ( x + 1 ) } { x - 1 }$

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)  $18 x ^ { 9 }$

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)  $- 27 x ^ { 3 }$

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)  $14 \mathrm { c }$

Question 11

Evaluate.
-$5 ^ { 3 }$

Accepted Answer

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)  $- 12 x + 45$

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)  $\frac { x ^ { 2 } + 7 x } { x + 4 }$

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)  $3 ( x + 6 ) ^ { 2 }$

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

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)  $\frac { 19 } { x }$

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)  $\frac { 1 } { \mathrm { x } ^ { 18 } }$

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)  $\frac { 1 } { 2 }$

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)  $( h - x ) k$

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)  $\frac { - 15 x ^ { 4 } } { y ^ { 5 } }$

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

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. - $\left( - 3 x ^ { 5 } y ^ { - 6 } \right) \left( 5 x ^ { - 1 } y \right)$

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)