Question 1

Write the expression in lowest terms.
-$$\frac { m ^ { 3 } - 8 } { m - 2 }$$

Accepted Answer

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

Question 2

Find the sum or difference.
-$$( p + 10 ) ^ { 2 }$$

Accepted Answer

A)  $100 p ^ { 2 } + 20 p + 100$ 
B)  $p ^ { 2 } + 100$ 
C)  $\mathrm { p } ^ { 2 } + 20 \mathrm { p } + 100$ 
D)  $p + 100$ 
A)  $100 p ^ { 2 } + 20 p + 100$ 
B)  $p ^ { 2 } + 100$ 
C)  $\mathrm { p } ^ { 2 } + 20 \mathrm { p } + 100$ 
D)  $p + 100$

Question 3

Find the sum or difference.
-$$( a - 11 ) ( a + 11 )$$

Accepted Answer

A)  $a ^ { 2 } + 22 a - 121$ 
B)  $a ^ { 2 } - 121$ 
C)  $a ^ { 2 } - 22 a - 121$ 
D)  $a ^ { 2 } - 22$ 
A)  $a ^ { 2 } + 22 a - 121$ 
B)  $a ^ { 2 } - 121$ 
C)  $a ^ { 2 } - 22 a - 121$ 
D)  $a ^ { 2 } - 22$

Question 4

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-A stone is dropped from a tower that is 730 feet high. The formula $h = 730 - 16 t ^ { 2 }$ describes the stone's height above the ground, $h$, in feet, $t$ seconds after it was dropped. What is the stone's height 1 seconds after it is released?

Accepted Answer

A)  739 ft 
B)  724 ft 
C)  714 ft 
D)  689 ft 
A)  739 ft 
B)  724 ft 
C)  714 ft 
D)  689 ft

Question 5

Simplify the expression. Assume all variables represent positive real numbers.
-$$5 \sqrt [ 3 ] { 27 x } + 5 \sqrt [ 3 ] { 64 x }$$

Accepted Answer

A)  $5 \sqrt [ 3 ] { 91 x }$ 
B)  $7 \sqrt [ 3 ] { x }$ 
C)  $35 \sqrt [ 3 ] { x }$ 
D)  $35 x$ 
A)  $5 \sqrt [ 3 ] { 91 x }$ 
B)  $7 \sqrt [ 3 ] { x }$ 
C)  $35 \sqrt [ 3 ] { x }$ 
D)  $35 x$

Question 6

Factor by any method.
-$$9 a ^ { 3 } - 16 a$$

Accepted Answer

A)  $a ( 3 a + 4 ) ( 3 a - 4 )$ 
B)  $\left( 3 a ^ { 2 } + 4 \right) ( 3 a - 4 )$ 
C)  $a ( 9 a + 1 ) ( a - 16 )$ 
D)  $a ( 3 a - 4 ) ^ { 2 }$ 
A)  $a ( 3 a + 4 ) ( 3 a - 4 )$ 
B)  $\left( 3 a ^ { 2 } + 4 \right) ( 3 a - 4 )$ 
C)  $a ( 9 a + 1 ) ( a - 16 )$ 
D)  $a ( 3 a - 4 ) ^ { 2 }$

Question 7

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }$

Accepted Answer

A)  $x ^ { 22 / 5 }$ 
B)  $x ^ { 34 / 5 }$ 
C)  $\frac { 1 } { x ^ { 34 / 5 } }$ 
D)  $\frac { 1 } { x ^ { 22 / 5 } }$ 
A)  $x ^ { 22 / 5 }$ 
B)  $x ^ { 34 / 5 }$ 
C)  $\frac { 1 } { x ^ { 34 / 5 } }$ 
D)  $\frac { 1 } { x ^ { 22 / 5 } }$

Question 8

Determine the degree of the polynomial.
-t - 3t2 + 6t3 + 5

Accepted Answer

A)  4 
B)  6 
C)  1 
D)  3 
A)  4 
B)  6 
C)  1 
D)  3

Question 9

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent
positive real numbers.
-$$\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }$$

Accepted Answer

A)  $x ^ { 22 / 7 }$ 
B)  $\frac { 1 } { x ^ { 22 / 7 } }$ 
C)  $x ^ { 11 / 5 }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 11 / 5 } }$ 
A)  $x ^ { 22 / 7 }$ 
B)  $\frac { 1 } { x ^ { 22 / 7 } }$ 
C)  $x ^ { 11 / 5 }$ 
D)  $\frac { 1 } { \mathrm { x } ^ { 11 / 5 } }$

Question 10

Find the sum or difference.
-$$\left( 3 m ^ { 4 } \right) \left( 2 m ^ { 4 } \right)$$

Accepted Answer

A)  $6 \mathrm {~m} ^ { 8 }$ 
B)  $- 6 m$ 
C)  $6 \mathrm {~m}$ 
D)  $- 6 m ^ { 8 }$ 
A)  $6 \mathrm {~m} ^ { 8 }$ 
B)  $- 6 m$ 
C)  $6 \mathrm {~m}$ 
D)  $- 6 m ^ { 8 }$

Question 11

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 16 s ^ { 7 } - 3 s - 4$

Accepted Answer

A)  Binomial 
B)  None of these 
C)  Monomial 
D)  Trinomial 
A)  Binomial 
B)  None of these 
C)  Monomial 
D)  Trinomial

Question 12

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 10 z ^ { 5 } + 6 z ^ { 4 } + 9 z ^ { 3 } + 12$

Accepted Answer

A)  Binomial 
B)  Trinomial 
C)  None of these 
D)  Monomial 
A)  Binomial 
B)  Trinomial 
C)  None of these 
D)  Monomial

Question 13

Find the sum or difference.
-$$( 9 m - 11 w ) ( 9 m + 11 w )$$

Accepted Answer

A)  $81 m ^ { 2 } + 198 m w - 121 w ^ { 2 }$ 
B)  $81 m ^ { 2 } - 198 m w - 121 w ^ { 2 }$ 
C)  $9 m ^ { 2 } - 11 w ^ { 2 }$ 
D)  $81 m ^ { 2 } - 121 w ^ { 2 }$ 
A)  $81 m ^ { 2 } + 198 m w - 121 w ^ { 2 }$ 
B)  $81 m ^ { 2 } - 198 m w - 121 w ^ { 2 }$ 
C)  $9 m ^ { 2 } - 11 w ^ { 2 }$ 
D)  $81 m ^ { 2 } - 121 w ^ { 2 }$

Question 14

Identify the set as finite or infinite.
-{6, 7, 8, . . ., 11}

Accepted Answer

A)  finite 
B)  infinite 
A)  finite 
B)  infinite

Question 15

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$( 2 + 3 ) + 6 = ( 3 + 2 ) + 6$

Accepted Answer

A)  Associative 
B)  Commutative 
C)  Distributive 
D)  Closure 
A)  Associative 
B)  Commutative 
C)  Distributive 
D)  Closure

Question 16

Factor by any method.
-$$x ^ { 6 } - 1$$

Accepted Answer

A)  $\left( x ^ { 2 } + 1 \right) \left( x ^ { 4 } - x ^ { 2 } + 1 \right)$ 
B)  $( x + 1 ) ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) \left( x ^ { 2 } - x + 1 \right)$ 
C)  $( x + 1 ) ( x - 1 ) \left( x ^ { 4 } + x ^ { 2 } + 1 \right)$ 
D)  $\left( x ^ { 3 } + 1 \right) \left( x ^ { 3 } - 1 \right)$ 
A)  $\left( x ^ { 2 } + 1 \right) \left( x ^ { 4 } - x ^ { 2 } + 1 \right)$ 
B)  $( x + 1 ) ( x - 1 ) \left( x ^ { 2 } + x + 1 \right) \left( x ^ { 2 } - x + 1 \right)$ 
C)  $( x + 1 ) ( x - 1 ) \left( x ^ { 4 } + x ^ { 2 } + 1 \right)$ 
D)  $\left( x ^ { 3 } + 1 \right) \left( x ^ { 3 } - 1 \right)$

Question 17

Factor by any method.
-$$y ^ { 2 } - 81$$

Accepted Answer

A)  $( \mathrm { y } + 9 ) ( \mathrm { y } - 9 )$ 
B)  $( y - 9 ) ( y - 9 )$ 
C)  $( \mathrm { y } + 81 ) ( \mathrm { y } - 81 )$ 
D)  $\left( y ^ { 2 } + 9 \right) \left( y ^ { 2 } - 9 \right)$ 
A)  $( \mathrm { y } + 9 ) ( \mathrm { y } - 9 )$ 
B)  $( y - 9 ) ( y - 9 )$ 
C)  $( \mathrm { y } + 81 ) ( \mathrm { y } - 81 )$ 
D)  $\left( y ^ { 2 } + 9 \right) \left( y ^ { 2 } - 9 \right)$

Question 18

Find the sum or difference.
-$\frac { 48 x ^ { 7 } - 36 x ^ { 6 } + 42 x ^ { 5 } } { 6 x ^ { 6 } }$

Accepted Answer

A)  $8 x - 36 x ^ { 6 } + \frac { 7 } { x }$ 
B)  $8 x - 6$ 
C)  $8 x - 6 + \frac { 7 } { x }$ 
D)  $15 x - 6$ 
A)  $8 x - 36 x ^ { 6 } + \frac { 7 } { x }$ 
B)  $8 x - 6$ 
C)  $8 x - 6 + \frac { 7 } { x }$ 
D)  $15 x - 6$

Question 19

Factor the trinomial, if possible.
-$$- 2 x ^ { 2 } - 6 x + 20$$

Accepted Answer

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

Question 20

Decide whether the expression has been simplified correctly.
-$6 ^ { 0 } x = 1$

Accepted Answer

A)  Not simplified correctly 
B)  Simplified correctly 
A)  Not simplified correctly 
B)  Simplified correctly

Write the expression in lowest terms. - $\frac { m ^ { 3 } - 8 } { m - 2 }$

Find the sum or difference. - $( p + 10 ) ^ { 2 }$

Find the sum or difference. - $( a - 11 ) ( a + 11 )$

Simplify the expression. Assume all variables represent positive real numbers. - $5 \sqrt [ 3 ] { 27 x } + 5 \sqrt [ 3 ] { 64 x }$

Factor by any method. - $9 a ^ { 3 } - 16 a$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }$

Determine the degree of the polynomial. -t - 3t2 + 6t3 + 5

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }$

Find the sum or difference. - $\left( 3 m ^ { 4 } \right) \left( 2 m ^ { 4 } \right)$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 16 s ^ { 7 } - 3 s - 4$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 10 z ^ { 5 } + 6 z ^ { 4 } + 9 z ^ { 3 } + 12$

Find the sum or difference. - $( 9 m - 11 w ) ( 9 m + 11 w )$

Identify the set as finite or infinite. -{6, 7, 8, . . ., 11}

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $( 2 + 3 ) + 6 = ( 3 + 2 ) + 6$

Factor by any method. - $x ^ { 6 } - 1$

Factor by any method. - $y ^ { 2 } - 81$

Find the sum or difference. - $\frac { 48 x ^ { 7 } - 36 x ^ { 6 } + 42 x ^ { 5 } } { 6 x ^ { 6 } }$

Factor the trinomial, if possible. - $- 2 x ^ { 2 } - 6 x + 20$

Decide whether the expression has been simplified correctly. - $6 ^ { 0 } x = 1$

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Exam 1: Review of Basic Concepts

Write the expression in lowest terms. - m3−8m−2\frac { m ^ { 3 } - 8 } { m - 2 }m−2m3−8​

Find the sum or difference. - (p+10)2( p + 10 ) ^ { 2 }(p+10)2

Find the sum or difference. - (a−11)(a+11)( a - 11 ) ( a + 11 )(a−11)(a+11)

Simplify the expression. Assume all variables represent positive real numbers. - 527x3+564x35 \sqrt [ 3 ] { 27 x } + 5 \sqrt [ 3 ] { 64 x }5327x​+5364x​

Factor by any method. - 9a3−16a9 a ^ { 3 } - 16 a9a3−16a

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - x3/5x6/5⋅x−5\frac { x ^ { 3 / 5 } } { x ^ { 6 / 5 } \cdot x ^ { - 5 } }x6/5⋅x−5x3/5​