Question 1

Factor by any method.
-$$\mathrm { p } ^ { 6 } + 1$$

Accepted Answer

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

Question 2

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 4 ] { \frac { 256 } { \mathrm { y } } }$$

Accepted Answer

A)  $\frac { 4 \sqrt [ 4 ] { y ^ { 3 } } } { y ^ { 2 } }$ 
B)  $\frac { 4 \sqrt [ 4 ] { y } } { y }$ 
C)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 2 } } } { \mathrm { y } }$ 
D)  $\frac { 4 \sqrt [ 4 ] { y ^ { 3 } } } { y }$ 
A)  $\frac { 4 \sqrt [ 4 ] { y ^ { 3 } } } { y ^ { 2 } }$ 
B)  $\frac { 4 \sqrt [ 4 ] { y } } { y }$ 
C)  $\frac { 4 \sqrt [ 4 ] { \mathrm { y } ^ { 2 } } } { \mathrm { y } }$ 
D)  $\frac { 4 \sqrt [ 4 ] { y ^ { 3 } } } { y }$

Question 3

Calculate the value mentally.
-$$\frac { 27 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }$$

Accepted Answer

A)  3 
B)  9 
C)  none of these 
D)  24 
A)  3 
B)  9 
C)  none of these 
D)  24

Question 4

Find the sum or difference.
-$$( - 2 + x ) ( 3 x + 1 )$$

Accepted Answer

A)  $x ^ { 2 } - 5 x - 5$ 
B)  $3 x ^ { 2 } - 5 x - 2$ 
C)  $3 x ^ { 2 } - 6 x - 2$ 
D)  $3 x ^ { 2 } - 2 x - 5$ 
A)  $x ^ { 2 } - 5 x - 5$ 
B)  $3 x ^ { 2 } - 5 x - 2$ 
C)  $3 x ^ { 2 } - 6 x - 2$ 
D)  $3 x ^ { 2 } - 2 x - 5$

Question 5

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$- 9 x ^ { 0 }$

Accepted Answer

A)  1 
B)  $- 1$ 
C)  $- 9$ 
D)  0 
A)  1 
B)  $- 1$ 
C)  $- 9$ 
D)  0

Question 6

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero
real numbers.
-$$\left( x ^ { - 8 } y ^ { 8 } \right) \left( x ^ { - 2 } y ^ { 5 } \right) ^ { - 1 }$$

Accepted Answer

A)  $\frac { y ^ { 4 } } { x ^ { 7 } }$ 
B)  $\frac { y ^ { 3 } } { x ^ { 6 } }$ 
C)  $\frac { x ^ { 6 } } { y ^ { 3 } }$ 
D)  $\frac { x ^ { 7 } } { y ^ { 4 } }$ 
A)  $\frac { y ^ { 4 } } { x ^ { 7 } }$ 
B)  $\frac { y ^ { 3 } } { x ^ { 6 } }$ 
C)  $\frac { x ^ { 6 } } { y ^ { 3 } }$ 
D)  $\frac { x ^ { 7 } } { y ^ { 4 } }$

Question 7

Simplify the expression.
-$\sqrt { 36 x ^ { 2 } }$

Accepted Answer

A)  $- 6 x$ 
B)  $36 x$ 
C)  $6 x ^ { 2 }$ 
D)  $6 | x |$ 
A)  $- 6 x$ 
B)  $36 x$ 
C)  $6 x ^ { 2 }$ 
D)  $6 | x |$

Question 8

Evaluate the expression.
-$$16 ^ { 1 / 4 }$$

Accepted Answer

A)  16 
B)  8 
C)  2 
D)  32 
A)  16 
B)  8 
C)  2 
D)  32

Question 9

Decide whether the expression has been simplified correctly.
-$\left( \frac { x } { 8 } \right) ^ { 5 } = \frac { x ^ { 5 } } { 8 }$

Accepted Answer

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

Question 10

Find the distance between two points given their coordinates.
-Find the distance between points $R$ and $S$ on a number line, with coordinates $- 2$ and 4 , respectively.

Accepted Answer

A)  $d ( R , S ) = 2$ 
B)  $d ( R , S ) = 6$ 
C)  $d ( R , S ) = - 2$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 6$ 
A)  $d ( R , S ) = 2$ 
B)  $d ( R , S ) = 6$ 
C)  $d ( R , S ) = - 2$ 
D)  $\mathrm { d } ( \mathrm { R } , \mathrm { S } ) = - 6$

Question 11

Evaluate the expression.
-$- | 20 |$

Accepted Answer

A)  $\pm 20$ 
B)  $- 20$ 
C)  0 
D)  20 
A)  $\pm 20$ 
B)  $- 20$ 
C)  0 
D)  20

Question 12

Factor out the greatest common factor. Simplify the factors, if possible.
-$48 x ^ { 8 } y ^ { 8 } - 84 x ^ { 4 } y ^ { 5 } + 24 x ^ { 6 } y ^ { 2 }$

Accepted Answer

A)  $12 x ^ { 4 } y ^ { 2 } \left( 4 x ^ { 4 } y ^ { 6 } - 7 y ^ { 3 } + 2 x ^ { 2 } \right)$ 
B)  $12 \left( 4 x ^ { 8 } y ^ { 8 } - 7 x ^ { 4 } y ^ { 5 } + 2 x ^ { 6 } y ^ { 2 } \right)$ 
C)  $12 x ^ { 4 } \left( 4 x ^ { 4 } y ^ { 8 } - 7 y ^ { 5 } + 2 x ^ { 2 } y ^ { 2 } \right)$ 
D)  $x ^ { 4 } y ^ { 2 } \left( 48 x ^ { 4 } y ^ { 6 } - 84 y ^ { 3 } + 24 x ^ { 2 } \right)$ 
A)  $12 x ^ { 4 } y ^ { 2 } \left( 4 x ^ { 4 } y ^ { 6 } - 7 y ^ { 3 } + 2 x ^ { 2 } \right)$ 
B)  $12 \left( 4 x ^ { 8 } y ^ { 8 } - 7 x ^ { 4 } y ^ { 5 } + 2 x ^ { 6 } y ^ { 2 } \right)$ 
C)  $12 x ^ { 4 } \left( 4 x ^ { 4 } y ^ { 8 } - 7 y ^ { 5 } + 2 x ^ { 2 } y ^ { 2 } \right)$ 
D)  $x ^ { 4 } y ^ { 2 } \left( 48 x ^ { 4 } y ^ { 6 } - 84 y ^ { 3 } + 24 x ^ { 2 } \right)$

Question 13

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers.
-$\frac { \left( x ^ { 2 } + 3 \right) ^ { 4 } ( 3 x ) - x ^ { 2 } ( 9 ) \left( x ^ { 2 } + 3 \right) ^ { 3 } ( 3 x ) } { \left( x ^ { 2 } + 3 \right) ^ { 8 } }$

Accepted Answer

A)  $\frac { ( 3 x ) \left( 3 - 8 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$ 
B)  $\frac { ( 3 x ) \left( 3 - 10 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$ 
C)  $\frac { ( 3 x ) \left( 3 + 8 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$ 
D)  $\frac { ( 3 x ) \left( 3 + 10 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$ 
A)  $\frac { ( 3 x ) \left( 3 - 8 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$ 
B)  $\frac { ( 3 x ) \left( 3 - 10 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$ 
C)  $\frac { ( 3 x ) \left( 3 + 8 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$ 
D)  $\frac { ( 3 x ) \left( 3 + 10 x ^ { 2 } \right) } { \left( x ^ { 2 } + 3 \right) ^ { 5 } }$

Question 14

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 17 x$

Accepted Answer

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

Question 15

Find the product or quotient.
-$$\frac { z ^ { 2 } + 11 z + 18 } { z ^ { 2 } + 14 z + 45 } + \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 8 z + 15 }$$

Accepted Answer

A)  $z + 3$ 
B)  $\frac { z + 3 } { z }$ 
C)  $\frac { z } { z ^ { 2 } + 14 z + 45 }$ 
D)  $\frac { z + 3 } { z ^ { 2 } + 5 z }$ 
A)  $z + 3$ 
B)  $\frac { z + 3 } { z }$ 
C)  $\frac { z } { z ^ { 2 } + 14 z + 45 }$ 
D)  $\frac { z + 3 } { z ^ { 2 } + 5 z }$

Question 16

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }$

Accepted Answer

A)  $\frac { \sqrt { 55 } + 2 \sqrt { 5 } } { 7 }$ 
B)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 13 }$ 
C)  $\frac { 3 \sqrt { 55 } + 115 } { 22 }$ 
D)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 7 }$ 
A)  $\frac { \sqrt { 55 } + 2 \sqrt { 5 } } { 7 }$ 
B)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 13 }$ 
C)  $\frac { 3 \sqrt { 55 } + 115 } { 22 }$ 
D)  $\frac { \sqrt { 55 } - 2 \sqrt { 5 } } { 7 }$

Question 17

Simplify the expression. Assume all variables represent positive real numbers.
-$6 \sqrt { 48 x ^ { 2 } } - 2 \sqrt { 27 x ^ { 2 } } - \sqrt { 3 x ^ { 2 } }$

Accepted Answer

A)  $17 x \sqrt { 3 }$ 
B)  $4 x \sqrt { 21 }$ 
C)  $3 x \sqrt { 21 }$ 
D)  $18 x \sqrt { 3 }$ 
A)  $17 x \sqrt { 3 }$ 
B)  $4 x \sqrt { 21 }$ 
C)  $3 x \sqrt { 21 }$ 
D)  $18 x \sqrt { 3 }$

Question 18

Factor the trinomial, if possible.
-$$64 m ^ { 2 } + 80 m + 25$$

Accepted Answer

A)  $( 8 m - 6 ) ^ { 2 }$ 
B)  $( 8 m + 5 ) ( 8 m - 5 )$ 
C)  $( 8 m - 5 ) ^ { 2 }$ 
D)  $( 8 m + 5 ) ^ { 2 }$ 
A)  $( 8 m - 6 ) ^ { 2 }$ 
B)  $( 8 m + 5 ) ( 8 m - 5 )$ 
C)  $( 8 m - 5 ) ^ { 2 }$ 
D)  $( 8 m + 5 ) ^ { 2 }$

Question 19

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

Accepted Answer

A)  $\pm 3$ 
B)  9 
C)  $- 3$ 
D)  not a real number 
A)  $\pm 3$ 
B)  9 
C)  $- 3$ 
D)  not a real number

Question 20

Evaluate the expression.
-$$- \left| - \frac { 8 } { 3 } \right|$$

Accepted Answer

A)  $\pm \frac { 8 } { 3 }$ 
B)  $- \frac { 8 } { 3 }$ 
C)  0 
D)  $\frac { 8 } { 3 }$ 
A)  $\pm \frac { 8 } { 3 }$ 
B)  $- \frac { 8 } { 3 }$ 
C)  0 
D)  $\frac { 8 } { 3 }$

Factor by any method. - $\mathrm { p } ^ { 6 } + 1$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 4 ] { \frac { 256 } { \mathrm { y } } }$

Calculate the value mentally. - $\frac { 27 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }$

Find the sum or difference. - $( - 2 + x ) ( 3 x + 1 )$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 9 x ^ { 0 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\left( x ^ { - 8 } y ^ { 8 } \right) \left( x ^ { - 2 } y ^ { 5 } \right) ^ { - 1 }$

Simplify the expression. - $\sqrt { 36 x ^ { 2 } }$

Evaluate the expression. - $16 ^ { 1 / 4 }$

Decide whether the expression has been simplified correctly. - $\left( \frac { x } { 8 } \right) ^ { 5 } = \frac { x ^ { 5 } } { 8 }$

Find the distance between two points given their coordinates. -Find the distance between points $R$ and $S$ on a number line, with coordinates $- 2$ and 4 , respectively.

Evaluate the expression. - $- | 20 |$

Factor out the greatest common factor. Simplify the factors, if possible. - $48 x ^ { 8 } y ^ { 8 } - 84 x ^ { 4 } y ^ { 5 } + 24 x ^ { 6 } y ^ { 2 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. - $\frac { \left( x ^ { 2 } + 3 \right) ^ { 4 } ( 3 x ) - x ^ { 2 } ( 9 ) \left( x ^ { 2 } + 3 \right) ^ { 3 } ( 3 x ) } { \left( x ^ { 2 } + 3 \right) ^ { 8 } }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 17 x$

Find the product or quotient. - $\frac { z ^ { 2 } + 11 z + 18 } { z ^ { 2 } + 14 z + 45 } + \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 8 z + 15 }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }$

Simplify the expression. Assume all variables represent positive real numbers. - $6 \sqrt { 48 x ^ { 2 } } - 2 \sqrt { 27 x ^ { 2 } } - \sqrt { 3 x ^ { 2 } }$

Factor the trinomial, if possible. - $64 m ^ { 2 } + 80 m + 25$

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

Evaluate the expression. - $- \left| - \frac { 8 } { 3 } \right|$

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 1: Review of Basic Concepts

Factor by any method. - p6+1\mathrm { p } ^ { 6 } + 1p6+1

Simplify the expression. Assume all variables represent positive real numbers. - 256y4\sqrt [ 4 ] { \frac { 256 } { \mathrm { y } } }4y256​​

Calculate the value mentally. - 271/231/2\frac { 27 ^ { 1 / 2 } } { 3 ^ { 1 / 2 } }31/2271/2​

Find the sum or difference. - (−2+x)(3x+1)( - 2 + x ) ( 3 x + 1 )(−2+x)(3x+1)

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - −9x0- 9 x ^ { 0 }−9x0

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - (x−8y8)(x−2y5)−1\left( x ^ { - 8 } y ^ { 8 } \right) \left( x ^ { - 2 } y ^ { 5 } \right) ^ { - 1 }(x−8y8)(x−2y5)−1

Simplify the expression. - 36x2\sqrt { 36 x ^ { 2 } }36x2​

Evaluate the expression. - 161/416 ^ { 1 / 4 }161/4

Decide whether the expression has been simplified correctly. - (x8)5=x58\left( \frac { x } { 8 } \right) ^ { 5 } = \frac { x ^ { 5 } } { 8 }(8x​)5=8x5​

Find the distance between two points given their coordinates. -Find the distance between points RRR and SSS on a number line, with coordinates −2- 2−2 and 4 , respectively.

Evaluate the expression. - −∣20∣- | 20 |−∣20∣

Factor out the greatest common factor. Simplify the factors, if possible. - 48x8y8−84x4y5+24x6y248 x ^ { 8 } y ^ { 8 } - 84 x ^ { 4 } y ^ { 5 } + 24 x ^ { 6 } y ^ { 2 }48x8y8−84x4y5+24x6y2

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −17x- 17 x−17x

Find the product or quotient. - z2+11z+18z2+14z+45+z2+2zz2+8z+15\frac { z ^ { 2 } + 11 z + 18 } { z ^ { 2 } + 14 z + 45 } + \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 8 z + 15 }z2+14z+45z2+11z+18​+z2+8z+15z2+2z​

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 511+2\frac { \sqrt { 5 } } { \sqrt { 11 } + 2 }11​+25​​

Simplify the expression. Assume all variables represent positive real numbers. - 648x2−227x2−3x26 \sqrt { 48 x ^ { 2 } } - 2 \sqrt { 27 x ^ { 2 } } - \sqrt { 3 x ^ { 2 } }648x2​−227x2​−3x2​

Factor the trinomial, if possible. - 64m2+80m+2564 m ^ { 2 } + 80 m + 2564m2+80m+25

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

Evaluate the expression. - −∣−83∣- \left| - \frac { 8 } { 3 } \right|−​−38​​