Question 1

Decide whether the expression has been simplified correctly.
-$x ^ { 3 } \cdot x ^ { 2 } = x ^ { 6 }$

Accepted Answer

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

Question 2

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real
numbers.
-$$\frac { 9 + \frac { 3 } { s } } { \frac { s } { 4 } + \frac { 1 } { 12 } }$$

Accepted Answer

A)  1 
B)  $\frac { \mathrm { s } } { 36 }$ 
C)  36 
D)  $\frac { 36 } { \mathrm {~s} }$ 
A)  1 
B)  $\frac { \mathrm { s } } { 36 }$ 
C)  36 
D)  $\frac { 36 } { \mathrm {~s} }$

Question 3

Write the expression in lowest terms.
-$$\frac { x ^ { 2 } + 4 x - 5 } { x ^ { 2 } - 4 x + 3 }$$

Accepted Answer

A)  $\frac { x + 5 } { x - 3 }$ 
B)  $\frac { x + 6 } { x - 2 }$ 
C)  $\frac { x - 5 } { x + 3 }$ 
D)  $\frac { x - 1 } { x + 1 }$ 
A)  $\frac { x + 5 } { x - 3 }$ 
B)  $\frac { x + 6 } { x - 2 }$ 
C)  $\frac { x - 5 } { x + 3 }$ 
D)  $\frac { x - 1 } { x + 1 }$

Question 4

Factor by grouping.
-$$6 x ^ { 2 } + 8 x y - 9 x y - 12 y ^ { 2 }$$

Accepted Answer

A)  $( 2 x - 3 y ) ( 3 x + 4 y )$ 
B)  $( 6 x - 3 y ) ( x + 4 y )$ 
C)  $( 2 x + 3 y ) ( 3 x + 4 y )$ 
D)  $( 2 x - 3 ) ( 3 x + 4 )$ 
A)  $( 2 x - 3 y ) ( 3 x + 4 y )$ 
B)  $( 6 x - 3 y ) ( x + 4 y )$ 
C)  $( 2 x + 3 y ) ( 3 x + 4 y )$ 
D)  $( 2 x - 3 ) ( 3 x + 4 )$

Question 5

Solve the problem.
-$$( 5 y + 5 ) \left( 3 y ^ { 3 } - 2 y ^ { 2 } - 5 y - 5 \right)$$

Accepted Answer

A)  $15 y ^ { 4 } - 20 y ^ { 3 } - 35 y ^ { 2 } - 50 y - 25$ 
B)  $15 y ^ { 4 } + 5 y ^ { 3 } - 35 y ^ { 2 } - 50 y - 25$ 
C)  $15 y ^ { 4 } + 5 y ^ { 3 } - 35 y ^ { 2 } - 25 y - 25$ 
D)  $15 y ^ { 4 } + 5 y ^ { 3 } - 50 y ^ { 2 } - 50 y - 25$ 
A)  $15 y ^ { 4 } - 20 y ^ { 3 } - 35 y ^ { 2 } - 50 y - 25$ 
B)  $15 y ^ { 4 } + 5 y ^ { 3 } - 35 y ^ { 2 } - 50 y - 25$ 
C)  $15 y ^ { 4 } + 5 y ^ { 3 } - 35 y ^ { 2 } - 25 y - 25$ 
D)  $15 y ^ { 4 } + 5 y ^ { 3 } - 50 y ^ { 2 } - 50 y - 25$

Question 6

Tell whether the statement is true or false.
-Let $A = \{ 9,10,11,12,13,14 \} , B = \{ 11,13,15 \} , C = \{ 9,10,12,14 \} , D = \{ 9,14 \}$, and $\mathrm { U } = \{ 9,10,11,12,13,14,15 \}$.
$$\{ 13,15 \} \subseteq B$$

Accepted Answer

A) True 
 B)False

Question 7

Write the expression in lowest terms.
-$$\frac { 15 x ^ { 3 } + 5 x } { 25 x ^ { 2 } }$$

Accepted Answer

A)  $\frac { 3 x ^ { 2 } + 1 } { 5 x }$ 
B)  $\frac { 3 x ^ { 2 } } { 5 x + 1 }$ 
C)  $\frac { 3 x + 1 } { 25 }$ 
D)  $3 x ^ { 2 } + 1$ 
A)  $\frac { 3 x ^ { 2 } + 1 } { 5 x }$ 
B)  $\frac { 3 x ^ { 2 } } { 5 x + 1 }$ 
C)  $\frac { 3 x + 1 } { 25 }$ 
D)  $3 x ^ { 2 } + 1$

Question 8

Factor the trinomial, if possible.
-$$7 x ^ { 2 } + 5 x + 2$$

Accepted Answer

A)  $( 7 x + 2 ) ( x - 1 )$ 
B)  $( 7 x + 1 ) ( x - 2 )$ 
C)  $( 7 x - 2 ) ( x + 1 )$ 
D)  prime 
A)  $( 7 x + 2 ) ( x - 1 )$ 
B)  $( 7 x + 1 ) ( x - 2 )$ 
C)  $( 7 x - 2 ) ( x + 1 )$ 
D)  prime

Question 9

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

Question 10

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are
rational, irrational, or nonreal complex.
-$$5 a ^ { 3 } x ^ { 7 } \left( - 3 a ^ { 6 } x ^ { 8 } - 7 x ^ { 4 } - 8 a \right)$$

Accepted Answer

A)  $- 15 a ^ { 18 } x ^ { 56 } + 35 a ^ { 3 } x ^ { 28 } + 40 a ^ { 3 } x ^ { 7 }$ 
B)  $15 a ^ { 9 } x ^ { 15 } + 35 a ^ { 3 } x ^ { 11 } + 40 a ^ { 4 } x ^ { 7 }$ 
C)  $- 15 a ^ { 9 } x ^ { 15 } - 7 x ^ { 4 } - 8 a$ 
D)  $- 15 a ^ { 9 } x ^ { 15 } - 35 a ^ { 3 } x ^ { 11 } - 40 a ^ { 4 } x ^ { 7 }$ 
A)  $- 15 a ^ { 18 } x ^ { 56 } + 35 a ^ { 3 } x ^ { 28 } + 40 a ^ { 3 } x ^ { 7 }$ 
B)  $15 a ^ { 9 } x ^ { 15 } + 35 a ^ { 3 } x ^ { 11 } + 40 a ^ { 4 } x ^ { 7 }$ 
C)  $- 15 a ^ { 9 } x ^ { 15 } - 7 x ^ { 4 } - 8 a$ 
D)  $- 15 a ^ { 9 } x ^ { 15 } - 35 a ^ { 3 } x ^ { 11 } - 40 a ^ { 4 } x ^ { 7 }$

Question 11

Solve the problem.
-$$\frac { 64 x ^ { 4 } - 48 x ^ { 3 } + 40 x ^ { 2 } } { 8 x ^ { 3 } }$$

Accepted Answer

A)  $8 x - 48 x ^ { 3 } + \frac { 5 } { x }$ 
B)  $8 x - 6$ 
C)  $8 x - 6 + \frac { 5 } { x }$ 
D)  $13 x - 6$ 
A)  $8 x - 48 x ^ { 3 } + \frac { 5 } { x }$ 
B)  $8 x - 6$ 
C)  $8 x - 6 + \frac { 5 } { x }$ 
D)  $13 x - 6$

Question 12

Write the expression in lowest terms.
-$$\frac { m ^ { 3 } - 64 } { m - 4 }$$

Accepted Answer

A)  $x ^ { 2 } - 16 x + 4$ 
B)  $x ^ { 2 } + 4 x + 16$ 
C)  $x ^ { 2 } - 4$ 
D)  $x ^ { 2 } + 16$ 
A)  $x ^ { 2 } - 16 x + 4$ 
B)  $x ^ { 2 } + 4 x + 16$ 
C)  $x ^ { 2 } - 4$ 
D)  $x ^ { 2 } + 16$

Question 13

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
--14x

Accepted Answer

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

Question 14

Factor out the greatest common factor. Simplify the factors, if possible.
-$$\mathrm { t } ( 8 - \mathrm { m } ) + \mathrm { s } ( 8 - \mathrm { m } )$$

Accepted Answer

A)  $( t + s ) ( 8 + m )$ 
B)  $t ( 8 - m ) + s$ 
C)  $( t + s ) ( 8 - m )$ 
D)  $( \mathrm { t } - \mathrm { s } ) ( 8 - \mathrm { m } )$ 
A)  $( t + s ) ( 8 + m )$ 
B)  $t ( 8 - m ) + s$ 
C)  $( t + s ) ( 8 - m )$ 
D)  $( \mathrm { t } - \mathrm { s } ) ( 8 - \mathrm { m } )$

Question 15

Evaluate the expression for x = -2, y = 3, and a = -4.
-$$\frac { y + 3 x } { y - 5 a }$$

Accepted Answer

A)  $- \frac { 1 } { 9 }$ 
B)  $- \frac { 5 } { 23 }$ 
C)  $- \frac { 3 } { 23 }$ 
D)  $- \frac { 2 } { 23 }$ 
A)  $- \frac { 1 } { 9 }$ 
B)  $- \frac { 5 } { 23 }$ 
C)  $- \frac { 3 } { 23 }$ 
D)  $- \frac { 2 } { 23 }$

Question 16

Simplify the expression. Assume all variables represent nonzero real numbers.
-$( - 2 x ) ^ { 3 }$

Accepted Answer

A)  $8 x$ 
B)  $- 8 x ^ { 3 }$ 
C)  $- 6 x$ 
D)  $6 x ^ { 3 }$ 
A)  $8 x$ 
B)  $- 8 x ^ { 3 }$ 
C)  $- 6 x$ 
D)  $6 x ^ { 3 }$

Question 17

Factor the trinomial, if possible.
-$$( x - 5 y ) ^ { 2 } + 6 ( x - 5 y ) + 9$$

Accepted Answer

A)  $( x + 5 y - 3 ) ( x - 5 y + 3 )$ 
B)  $( x - 5 y + 3 ) ^ { 2 }$ 
C)  $( x - 5 y - 3 ) ^ { 2 }$ 
D)  $( x + 5 y + 3 ) ^ { 2 }$ 
A)  $( x + 5 y - 3 ) ( x - 5 y + 3 )$ 
B)  $( x - 5 y + 3 ) ^ { 2 }$ 
C)  $( x - 5 y - 3 ) ^ { 2 }$ 
D)  $( x + 5 y + 3 ) ^ { 2 }$

Question 18

Simplify the expression. Assume all variables represent positive real numbers.
-$$\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 16 } y ^ { 8 } }$$

Accepted Answer

A)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x ^ { 2 } y }$ 
B)  $x ^ { 5 } y ^ { 5 } \sqrt [ 3 ] { x y }$ 
C)  $x ^ { 5 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$ 
D)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x y ^ { 2 } }$ 
A)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x ^ { 2 } y }$ 
B)  $x ^ { 5 } y ^ { 5 } \sqrt [ 3 ] { x y }$ 
C)  $x ^ { 5 } y ^ { 6 } \sqrt [ 3 ] { x ^ { 2 } y ^ { 2 } }$ 
D)  $x ^ { 5 } y ^ { 4 } \sqrt [ 3 ] { x y ^ { 2 } }$

Question 19

Identify the expression as a polynomial or not a polynomial.
--1

Accepted Answer

A)  Not a polynomial 
B)  Polynomial 
A)  Not a polynomial 
B)  Polynomial

Question 20

Evaluate the expression.
-$256 ^ { 5 / 4 }$

Accepted Answer

A)  1024 
B)  16,384 
C)  262,144 
D)  65,536 
A)  1024 
B)  16,384 
C)  262,144 
D)  65,536

Decide whether the expression has been simplified correctly. - $x ^ { 3 } \cdot x ^ { 2 } = x ^ { 6 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $\frac { 9 + \frac { 3 } { s } } { \frac { s } { 4 } + \frac { 1 } { 12 } }$

Write the expression in lowest terms. - $\frac { x ^ { 2 } + 4 x - 5 } { x ^ { 2 } - 4 x + 3 }$

Factor by grouping. - $6 x ^ { 2 } + 8 x y - 9 x y - 12 y ^ { 2 }$

Solve the problem. - $( 5 y + 5 ) \left( 3 y ^ { 3 } - 2 y ^ { 2 } - 5 y - 5 \right)$

Tell whether the statement is true or false. -Let $A = \{ 9,10,11,12,13,14 \} , B = \{ 11,13,15 \} , C = \{ 9,10,12,14 \} , D = \{ 9,14 \}$ , and $\mathrm { U } = \{ 9,10,11,12,13,14,15 \}$ . $\{ 13,15 \} \subseteq B$

Write the expression in lowest terms. - $\frac { 15 x ^ { 3 } + 5 x } { 25 x ^ { 2 } }$

Factor the trinomial, if possible. - $7 x ^ { 2 } + 5 x + 2$

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

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - $5 a ^ { 3 } x ^ { 7 } \left( - 3 a ^ { 6 } x ^ { 8 } - 7 x ^ { 4 } - 8 a \right)$

Solve the problem. - $\frac { 64 x ^ { 4 } - 48 x ^ { 3 } + 40 x ^ { 2 } } { 8 x ^ { 3 } }$

Write the expression in lowest terms. - $\frac { m ^ { 3 } - 64 } { m - 4 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. --14x

Factor out the greatest common factor. Simplify the factors, if possible. - $\mathrm { t } ( 8 - \mathrm { m } ) + \mathrm { s } ( 8 - \mathrm { m } )$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { y + 3 x } { y - 5 a }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $( - 2 x ) ^ { 3 }$

Factor the trinomial, if possible. - $( x - 5 y ) ^ { 2 } + 6 ( x - 5 y ) + 9$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { x y ^ { 5 } } \cdot \sqrt [ 3 ] { x ^ { 16 } y ^ { 8 } }$

Identify the expression as a polynomial or not a polynomial. --1

Evaluate the expression. - $256 ^ { 5 / 4 }$

Equations and Inequalities

Graphs and Functions

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 1: Review of Basic Concepts

Decide whether the expression has been simplified correctly. - x3⋅x2=x6x ^ { 3 } \cdot x ^ { 2 } = x ^ { 6 }x3⋅x2=x6

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 9+3ss4+112\frac { 9 + \frac { 3 } { s } } { \frac { s } { 4 } + \frac { 1 } { 12 } }4s​+121​9+s3​​

Write the expression in lowest terms. - x2+4x−5x2−4x+3\frac { x ^ { 2 } + 4 x - 5 } { x ^ { 2 } - 4 x + 3 }x2−4x+3x2+4x−5​

Factor by grouping. - 6x2+8xy−9xy−12y26 x ^ { 2 } + 8 x y - 9 x y - 12 y ^ { 2 }6x2+8xy−9xy−12y2

Solve the problem. - (5y+5)(3y3−2y2−5y−5)( 5 y + 5 ) \left( 3 y ^ { 3 } - 2 y ^ { 2 } - 5 y - 5 \right)(5y+5)(3y3−2y2−5y−5)

Write the expression in lowest terms. - 15x3+5x25x2\frac { 15 x ^ { 3 } + 5 x } { 25 x ^ { 2 } }25x215x3+5x​

Factor the trinomial, if possible. - 7x2+5x+27 x ^ { 2 } + 5 x + 27x2+5x+2

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​​

Evaluate the discriminant for the equation. Then use it to predict the number of distinct solutions, and whether they are rational, irrational, or nonreal complex. - 5a3x7(−3a6x8−7x4−8a)5 a ^ { 3 } x ^ { 7 } \left( - 3 a ^ { 6 } x ^ { 8 } - 7 x ^ { 4 } - 8 a \right)5a3x7(−3a6x8−7x4−8a)

Solve the problem. - 64x4−48x3+40x28x3\frac { 64 x ^ { 4 } - 48 x ^ { 3 } + 40 x ^ { 2 } } { 8 x ^ { 3 } }8x364x4−48x3+40x2​

Write the expression in lowest terms. - m3−64m−4\frac { m ^ { 3 } - 64 } { m - 4 }m−4m3−64​