Question 1

Find the sum or difference.
-$$\left( 2 x ^ { 3 } - x ^ { 2 } + 3 x - 1 \right) ( 2 x + 2 )$$

Accepted Answer

A)  $3 x ^ { 4 } + 6 x ^ { 3 } + 6 x ^ { 2 } + 6 x - 4$ 
B)  $4 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 4 x - 2$ 
C)  $4 x ^ { 3 } + 2 x ^ { 2 } + 4 x + 4$ 
D)  $5 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } - 4 x + 2$ 
A)  $3 x ^ { 4 } + 6 x ^ { 3 } + 6 x ^ { 2 } + 6 x - 4$ 
B)  $4 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 4 x - 2$ 
C)  $4 x ^ { 3 } + 2 x ^ { 2 } + 4 x + 4$ 
D)  $5 x ^ { 4 } - 2 x ^ { 3 } + 3 x ^ { 2 } - 4 x + 2$

Question 2

Find the sum or difference.
-$11 a x ^ { 6 } \left( - 4 a x ^ { 7 } - 2 x ^ { 5 } - 12 a \right)$

Accepted Answer

A)  $- 44 a ^ { 2 } x ^ { 13 } - 22 a x ^ { 11 } - 132 a ^ { 2 } x ^ { 6 }$ 
B)  $- 44 a ^ { 2 } x ^ { 13 } + 22 a x ^ { 11 } + 132 a ^ { 2 } x ^ { 6 }$ 
C)  $- 44 a ^ { 2 } x ^ { 42 } - 22 a x ^ { 30 } - 132 a ^ { 2 } x ^ { 6 }$ 
D)  $- 44 a x ^ { 13 } - 22 a x ^ { 11 } - 132 a x ^ { 6 }$ 
A)  $- 44 a ^ { 2 } x ^ { 13 } - 22 a x ^ { 11 } - 132 a ^ { 2 } x ^ { 6 }$ 
B)  $- 44 a ^ { 2 } x ^ { 13 } + 22 a x ^ { 11 } + 132 a ^ { 2 } x ^ { 6 }$ 
C)  $- 44 a ^ { 2 } x ^ { 42 } - 22 a x ^ { 30 } - 132 a ^ { 2 } x ^ { 6 }$ 
D)  $- 44 a x ^ { 13 } - 22 a x ^ { 11 } - 132 a x ^ { 6 }$

Question 3

Factor the trinomial, if possible.
-$10 m ^ { 2 } + 37 m n + 30 n ^ { 2 }$

Accepted Answer

A)  $( 2 m - 5 n ) ( 5 m - 6 n )$ 
B)  $\left( 2 m + 5 n ^ { 2 } \right) ( 5 m + 6 )$ 
C)  $( 2 m + 6 n ) ( 5 m + 5 n )$ 
D)  $( 2 m + 5 n ) ( 5 m + 6 n )$ 
A)  $( 2 m - 5 n ) ( 5 m - 6 n )$ 
B)  $\left( 2 m + 5 n ^ { 2 } \right) ( 5 m + 6 )$ 
C)  $( 2 m + 6 n ) ( 5 m + 5 n )$ 
D)  $( 2 m + 5 n ) ( 5 m + 6 n )$

Question 4

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$$\frac { 3 } { 5 - \sqrt { 3 } }$$

Accepted Answer

A)  $\frac { 15 - 3 \sqrt { 3 } } { 22 }$ 
B)  $\frac { 15 + 3 \sqrt { 3 } } { 22 }$ 
C)  $\frac { 15 + 3 \sqrt { 3 } } { 2 }$ 
D)  $\frac { 3 } { 5 } - \frac { 3 } { \sqrt { 3 } }$ 
A)  $\frac { 15 - 3 \sqrt { 3 } } { 22 }$ 
B)  $\frac { 15 + 3 \sqrt { 3 } } { 22 }$ 
C)  $\frac { 15 + 3 \sqrt { 3 } } { 2 }$ 
D)  $\frac { 3 } { 5 } - \frac { 3 } { \sqrt { 3 } }$

Question 5

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt { 96 x ^ { 2 } y }$

Accepted Answer

A)  $4 x y ^ { 2 } \sqrt { 6 }$ 
B)  $4 x y \sqrt { 6 }$ 
C)  $4 x ^ { 2 } \sqrt { 6 y }$ 
D)  $4 x \sqrt { 6 y }$ 
A)  $4 x y ^ { 2 } \sqrt { 6 }$ 
B)  $4 x y \sqrt { 6 }$ 
C)  $4 x ^ { 2 } \sqrt { 6 y }$ 
D)  $4 x \sqrt { 6 y }$

Question 6

Write the expression in lowest terms.
-$\frac { 15 x ^ { 3 } - 6 x } { 9 x ^ { 2 } }$

Accepted Answer

A)  $5 x ^ { 2 } - 2$ 
B)  $\frac { 5 x - 2 } { 9 }$ 
C)  $\frac { 5 x ^ { 2 } } { 3 x - 2 }$ 
D)  $\frac { 5 x ^ { 2 } - 2 } { 3 x }$ 
A)  $5 x ^ { 2 } - 2$ 
B)  $\frac { 5 x - 2 } { 9 }$ 
C)  $\frac { 5 x ^ { 2 } } { 3 x - 2 }$ 
D)  $\frac { 5 x ^ { 2 } - 2 } { 3 x }$

Question 7

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$( - 2 ) ^ { - 6 }$$

Accepted Answer

A)  $\frac { 1 } { 64 }$ 
B)  64 
C)  $ - \frac { 1 } { 64 }$ 
D)  $- 64$ 
A)  $\frac { 1 } { 64 }$ 
B)  64 
C)  $ - \frac { 1 } { 64 }$ 
D)  $- 64$

Question 8

Decide whether the expression has been simplified correctly.
-$\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 8 }$

Accepted Answer

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

Question 9

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-The radius of a sphere is given by the formula $\mathrm { r } = \sqrt { \frac { \mathrm { S } } { 4 \pi } }$, where $\mathrm { S }$ is the surface area. If the surface area is 14,607 square inches, what is the radius? Use $3.14$ for $\pi$, and round your answer to the nearest tenth of an inch.

Accepted Answer

A)  60.4 in. 
B)  34.1 in. 
C)  0 in. 
D)  107.1 in. 
A)  60.4 in. 
B)  34.1 in. 
C)  0 in. 
D)  107.1 in.

Question 10

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 19 x ^ { 4 } - 4 w ^ { 3 } + 8 w + 4 y ^ { 5 } + 3$

Accepted Answer

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

Question 11

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$\frac { \frac { 3 } { y } } { \frac { 2 } { y + 3 } }$

Accepted Answer

A)  $\frac { 2 y } { 3 ( y + 3 ) }$ 
B)  $\frac { 3 ( y + 3 ) } { 2 y }$ 
C)  $\frac { y + 3 } { 6 y }$ 
D)  $6 y ( y + 3 )$ 
A)  $\frac { 2 y } { 3 ( y + 3 ) }$ 
B)  $\frac { 3 ( y + 3 ) } { 2 y }$ 
C)  $\frac { y + 3 } { 6 y }$ 
D)  $6 y ( y + 3 )$

Question 12

Find the sum or difference.
-$$( x + 1 ) ( 3 x + 6 )$$

Accepted Answer

A)  $3 x ^ { 2 } + 6 x + 9$ 
B)  $3 x ^ { 2 } + 9 x + 6$ 
C)  $x ^ { 2 } + 9 x + 9$ 
D)  $3 x ^ { 2 } + 8 x + 6$ 
A)  $3 x ^ { 2 } + 6 x + 9$ 
B)  $3 x ^ { 2 } + 9 x + 6$ 
C)  $x ^ { 2 } + 9 x + 9$ 
D)  $3 x ^ { 2 } + 8 x + 6$

Question 13

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt [ 3 ] { 27 x y ^ { 2 } } \cdot \sqrt [ 3 ] { 3 y ^ { 2 } } } { \sqrt [ 3 ] { 243 x y ^ { 4 } } }$$

Accepted Answer

A)  $\sqrt [ 3 ] { 3 }$ 
B)  $\frac { \sqrt [ 3 ] { 9 } } { 9 }$ 
C)  $\frac { \sqrt [ 3 ] { 3 } } { 3 }$ 
D)  $\frac { \sqrt [ 3 ] { 9 } } { 3 }$ 
A)  $\sqrt [ 3 ] { 3 }$ 
B)  $\frac { \sqrt [ 3 ] { 9 } } { 9 }$ 
C)  $\frac { \sqrt [ 3 ] { 3 } } { 3 }$ 
D)  $\frac { \sqrt [ 3 ] { 9 } } { 3 }$

Question 14

Find the sum or difference.
-$$\left( 2 x ^ { 7 } + 6 x ^ { 9 } - 7 - 7 x ^ { 8 } \right) - \left( 2 - 2 x ^ { 8 } + 3 x ^ { 9 } - 7 x ^ { 7 } \right)$$

Accepted Answer

A)  $9 x ^ { 9 } - 9 x ^ { 8 } - 5 x ^ { 7 } - 5$ 
B)  $3 x ^ { 9 } - 9 x ^ { 8 } - 5 x ^ { 7 } - 5$ 
C)  $9 x ^ { 9 } - 9 x ^ { 8 } - 5 x ^ { 7 } - 9$ 
D)  $3 x ^ { 9 } - 5 x ^ { 8 } + 9 x ^ { 7 } - 9$ 
A)  $9 x ^ { 9 } - 9 x ^ { 8 } - 5 x ^ { 7 } - 5$ 
B)  $3 x ^ { 9 } - 9 x ^ { 8 } - 5 x ^ { 7 } - 5$ 
C)  $9 x ^ { 9 } - 9 x ^ { 8 } - 5 x ^ { 7 } - 9$ 
D)  $3 x ^ { 9 } - 5 x ^ { 8 } + 9 x ^ { 7 } - 9$

Question 15

Simplify the expression.
-$\sqrt { ( z - 6 ) ^ { 2 } }$

Accepted Answer

A)  $| z - 6 |$ 
B)  $z - 6$ 
C)  $| z | - 6$ 
D)  $6 - \mathrm { z }$ 
A)  $| z - 6 |$ 
B)  $z - 6$ 
C)  $| z | - 6$ 
D)  $6 - \mathrm { z }$

Question 16

Find the distance between two points given their coordinates.
-Find the distance between points $P$ and $Q$ on a number line, with coordinates $- 10$ and 3 , respectively.

Accepted Answer

A)  $\mathrm { d } ( \mathrm { P } , \mathrm { Q } ) = - 13$ 
B)  $\mathrm { d } ( P , Q ) = 7$ 
C)  $\mathrm { d } ( \mathrm { P } , \mathrm { Q } ) = - 7$ 
D)  $\mathrm { d } ( \mathrm { P } , \mathrm { Q } ) = 13$ 
A)  $\mathrm { d } ( \mathrm { P } , \mathrm { Q } ) = - 13$ 
B)  $\mathrm { d } ( P , Q ) = 7$ 
C)  $\mathrm { d } ( \mathrm { P } , \mathrm { Q } ) = - 7$ 
D)  $\mathrm { d } ( \mathrm { P } , \mathrm { Q } ) = 13$

Question 17

Factor by any method.
-$$4 x ^ { 2 } - 4 x + 1 - y ^ { 2 }$$

Accepted Answer

A)  $( 2 x + 1 + y ) ( 2 x + 1 - y )$ 
B)  $( 2 x - 1 + y ) ( 2 x + 1 - y )$ 
C)  $( 2 x - 1 + y ) ( 2 x - 1 - y )$ 
D)  prime 
A)  $( 2 x + 1 + y ) ( 2 x + 1 - y )$ 
B)  $( 2 x - 1 + y ) ( 2 x + 1 - y )$ 
C)  $( 2 x - 1 + y ) ( 2 x - 1 - y )$ 
D)  prime

Question 18

Find the sum or difference.
-$$\frac { 12 x ^ { 8 } - 16 x ^ { 4 } } { - 4 x ^ { 8 } }$$

Accepted Answer

A)  $12 x ^ { 8 } + \frac { 4 } { x ^ { 4 } }$ 
B)  $- 3 + \frac { 4 } { x ^ { 4 } }$ 
C)  $- 3 + 4 x ^ { 4 }$ 
D)  $- 3 - 16 \mathrm { x } ^ { 4 }$ 
A)  $12 x ^ { 8 } + \frac { 4 } { x ^ { 4 } }$ 
B)  $- 3 + \frac { 4 } { x ^ { 4 } }$ 
C)  $- 3 + 4 x ^ { 4 }$ 
D)  $- 3 - 16 \mathrm { x } ^ { 4 }$

Question 19

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

Accepted Answer

A)  $8 \mathrm {~m}$ 
B)  $- 8 m ^ { 5 }$ 
C)  $8 m ^ { 6 }$ 
D)  $- 8 m$ 
A)  $8 \mathrm {~m}$ 
B)  $- 8 m ^ { 5 }$ 
C)  $8 m ^ { 6 }$ 
D)  $- 8 m$

Question 20

Evaluate the expression for x $$x = - 2 , y = 3 , \text { and } a = - 4$$
-$$\frac { 2 x + 2 ( 3 + a ) ^ { 2 } } { y - 1 }$$

Accepted Answer

A)  19 
B)  9 
C)  $- 1$ 
D)  33 
A)  19 
B)  9 
C)  $- 1$ 
D)  33

Find the sum or difference. - $\left( 2 x ^ { 3 } - x ^ { 2 } + 3 x - 1 \right) ( 2 x + 2 )$

Find the sum or difference. - $11 a x ^ { 6 } \left( - 4 a x ^ { 7 } - 2 x ^ { 5 } - 12 a \right)$

Factor the trinomial, if possible. - $10 m ^ { 2 } + 37 m n + 30 n ^ { 2 }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 3 } { 5 - \sqrt { 3 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { 96 x ^ { 2 } y }$

Write the expression in lowest terms. - $\frac { 15 x ^ { 3 } - 6 x } { 9 x ^ { 2 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 2 ) ^ { - 6 }$

Decide whether the expression has been simplified correctly. - $\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 8 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 19 x ^ { 4 } - 4 w ^ { 3 } + 8 w + 4 y ^ { 5 } + 3$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { \frac { 3 } { y } } { \frac { 2 } { y + 3 } }$

Find the sum or difference. - $( x + 1 ) ( 3 x + 6 )$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt [ 3 ] { 27 x y ^ { 2 } } \cdot \sqrt [ 3 ] { 3 y ^ { 2 } } } { \sqrt [ 3 ] { 243 x y ^ { 4 } } }$

Find the sum or difference. - $\left( 2 x ^ { 7 } + 6 x ^ { 9 } - 7 - 7 x ^ { 8 } \right) - \left( 2 - 2 x ^ { 8 } + 3 x ^ { 9 } - 7 x ^ { 7 } \right)$

Simplify the expression. - $\sqrt { ( z - 6 ) ^ { 2 } }$

Find the distance between two points given their coordinates. -Find the distance between points $P$ and $Q$ on a number line, with coordinates $- 10$ and 3 , respectively.

Factor by any method. - $4 x ^ { 2 } - 4 x + 1 - y ^ { 2 }$

Find the sum or difference. - $\frac { 12 x ^ { 8 } - 16 x ^ { 4 } } { - 4 x ^ { 8 } }$

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

Evaluate the expression for x $x = - 2 , y = 3 , \text { and } a = - 4$ - $\frac { 2 x + 2 ( 3 + a ) ^ { 2 } } { y - 1 }$

Equations and Inequalities

Graphs and Functions

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

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Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 1: Review of Basic Concepts

Find the sum or difference. - (2x3−x2+3x−1)(2x+2)\left( 2 x ^ { 3 } - x ^ { 2 } + 3 x - 1 \right) ( 2 x + 2 )(2x3−x2+3x−1)(2x+2)

Find the sum or difference. - 11ax6(−4ax7−2x5−12a)11 a x ^ { 6 } \left( - 4 a x ^ { 7 } - 2 x ^ { 5 } - 12 a \right)11ax6(−4ax7−2x5−12a)

Factor the trinomial, if possible. - 10m2+37mn+30n210 m ^ { 2 } + 37 m n + 30 n ^ { 2 }10m2+37mn+30n2

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 35−3\frac { 3 } { 5 - \sqrt { 3 } }5−3​3​

Simplify the expression. Assume all variables represent positive real numbers. - 96x2y\sqrt { 96 x ^ { 2 } y }96x2y​

Write the expression in lowest terms. - 15x3−6x9x2\frac { 15 x ^ { 3 } - 6 x } { 9 x ^ { 2 } }9x215x3−6x​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - (−2)−6( - 2 ) ^ { - 6 }(−2)−6

Decide whether the expression has been simplified correctly. - (x4)2=x8\left( x ^ { 4 } \right) ^ { 2 } = x ^ { 8 }(x4)2=x8

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −19x4−4w3+8w+4y5+3- 19 x ^ { 4 } - 4 w ^ { 3 } + 8 w + 4 y ^ { 5 } + 3−19x4−4w3+8w+4y5+3

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 3y2y+3\frac { \frac { 3 } { y } } { \frac { 2 } { y + 3 } }y+32​y3​​

Find the sum or difference. - (x+1)(3x+6)( x + 1 ) ( 3 x + 6 )(x+1)(3x+6)

Simplify the expression. Assume all variables represent positive real numbers. - 27xy23⋅3y23243xy43\frac { \sqrt [ 3 ] { 27 x y ^ { 2 } } \cdot \sqrt [ 3 ] { 3 y ^ { 2 } } } { \sqrt [ 3 ] { 243 x y ^ { 4 } } }3243xy4​327xy2​⋅33y2​​

Find the sum or difference. - (2x7+6x9−7−7x8)−(2−2x8+3x9−7x7)\left( 2 x ^ { 7 } + 6 x ^ { 9 } - 7 - 7 x ^ { 8 } \right) - \left( 2 - 2 x ^ { 8 } + 3 x ^ { 9 } - 7 x ^ { 7 } \right)(2x7+6x9−7−7x8)−(2−2x8+3x9−7x7)

Simplify the expression. - (z−6)2\sqrt { ( z - 6 ) ^ { 2 } }(z−6)2​

Find the distance between two points given their coordinates. -Find the distance between points PPP and QQQ on a number line, with coordinates −10- 10−10 and 3 , respectively.

Factor by any method. - 4x2−4x+1−y24 x ^ { 2 } - 4 x + 1 - y ^ { 2 }4x2−4x+1−y2

Find the sum or difference. - 12x8−16x4−4x8\frac { 12 x ^ { 8 } - 16 x ^ { 4 } } { - 4 x ^ { 8 } }−4x812x8−16x4​

Find the sum or difference. - (−2m2)(4m3)\left( - 2 m ^ { 2 } \right) \left( 4 m ^ { 3 } \right)(−2m2)(4m3)

Evaluate the expression for x x=−2,y=3, and a=−4x = - 2 , y = 3 , \text { and } a = - 4x=−2,y=3, and a=−4 - 2x+2(3+a)2y−1\frac { 2 x + 2 ( 3 + a ) ^ { 2 } } { y - 1 }y−12x+2(3+a)2​