Question 1

Factor the trinomial, if possible.
-$$( m - 3 n ) ^ { 2 } - 8 ( m - 3 n ) + 16$$

Accepted Answer

A)  $( m - 3 n + 4 ) ( m + 3 n - 4 )$ 
B)  $( m - 3 n ) ^ { 2 }$ 
C)  $( m - 3 n - 4 ) ^ { 2 }$ 
D)  $( \mathrm { m } + 3 \mathrm { n } + 4 ) ^ { 2 }$ 
A)  $( m - 3 n + 4 ) ( m + 3 n - 4 )$ 
B)  $( m - 3 n ) ^ { 2 }$ 
C)  $( m - 3 n - 4 ) ^ { 2 }$ 
D)  $( \mathrm { m } + 3 \mathrm { n } + 4 ) ^ { 2 }$

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0.
-Find the magnitude of the difference between a windchill factor of $- 50$ and a windchill factor of $- 5$.

Accepted Answer

A)  $- 45$ 
B)  55 
C)  45 
D)  $- 55$ 
A)  $- 45$ 
B)  55 
C)  45 
D)  $- 55$

Question 4

Find the product or quotient.
-$$\frac { ( x - y ) ^ { 2 } - 49 } { ( x + y ) ^ { 2 } - 49 } + \frac { x - y - 7 } { x + y + 7 }$$

Accepted Answer

A)  $\frac { x + y + 7 } { x - y - 7 }$ 
B)  $x - y + 7$ 
C)  $\frac { x - y + 7 } { x + y - 7 }$ 
D)  $- 1$ 
A)  $\frac { x + y + 7 } { x - y - 7 }$ 
B)  $x - y + 7$ 
C)  $\frac { x - y + 7 } { x + y - 7 }$ 
D)  $- 1$

Question 5

Tell whether the statement is true or false.
-$\{ 5,7,8,10 \} \cap \varnothing = \{ 5,7,8,10 \}$

Accepted Answer

A) True 
 B)False

Question 6

Factor by any method.
-$15 x ^ { 10 } + 18 x ^ { 5 } y ^ { 4 } + 20 x ^ { 5 } y ^ { 4 } + 24 y ^ { 8 }$

Accepted Answer

A)  $\left( 3 x ^ { 5 } - 4 y ^ { 4 } \right) \left( 5 x ^ { 5 } - 6 y ^ { 4 } \right)$ 
B)  $\left( 15 x ^ { 5 } + 4 y ^ { 4 } \right) \left( x ^ { 5 } + 6 y ^ { 4 } \right)$ 
C)  $\left( 3 x ^ { 5 } + 4 y ^ { 4 } \right) \left( 5 x ^ { 5 } + 6 y ^ { 4 } \right)$ 
D)  $\left( 3 x ^ { 5 } + 4 y \right) \left( 5 x ^ { 5 } + 6 y ^ { 8 } \right)$ 
A)  $\left( 3 x ^ { 5 } - 4 y ^ { 4 } \right) \left( 5 x ^ { 5 } - 6 y ^ { 4 } \right)$ 
B)  $\left( 15 x ^ { 5 } + 4 y ^ { 4 } \right) \left( x ^ { 5 } + 6 y ^ { 4 } \right)$ 
C)  $\left( 3 x ^ { 5 } + 4 y ^ { 4 } \right) \left( 5 x ^ { 5 } + 6 y ^ { 4 } \right)$ 
D)  $\left( 3 x ^ { 5 } + 4 y \right) \left( 5 x ^ { 5 } + 6 y ^ { 8 } \right)$

Question 7

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 18 y ^ { 3 } + 6 y ^ { 2 } + - 5$

Accepted Answer

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

Question 8

Find the sum or difference.
-$\left( 4 a ^ { 4 } - 7 a ^ { 2 } \right) + \left( 8 a ^ { 4 } - 3 a ^ { 2 } \right)$

Accepted Answer

A)  $12 a ^ { 4 } - 10 a ^ { 2 }$ 
B)  $2 \mathrm { a } 12$ 
C)  $2 a ^ { 6 }$ 
D)  $12 a ^ { 8 } - 10 a ^ { 4 }$ 
A)  $12 a ^ { 4 } - 10 a ^ { 2 }$ 
B)  $2 \mathrm { a } 12$ 
C)  $2 a ^ { 6 }$ 
D)  $12 a ^ { 8 } - 10 a ^ { 4 }$

Question 9

Identify the property illustrated by the statement. Assume all variables represent real numbers.
-$6 ( \pi ) \text { is a real number. }$

Accepted Answer

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

Question 10

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not
zero.
-$\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$

Accepted Answer

A)  $\frac { 4 ( \sqrt { x + h } + \sqrt { x } ) } { h }$ 
B)  $\frac { 4 ( \sqrt { x + h } - \sqrt { x } ) } { h }$ 
C)  $\frac { 4 \sqrt { h } } { h }$ 
D)  $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$ 
A)  $\frac { 4 ( \sqrt { x + h } + \sqrt { x } ) } { h }$ 
B)  $\frac { 4 ( \sqrt { x + h } - \sqrt { x } ) } { h }$ 
C)  $\frac { 4 \sqrt { h } } { h }$ 
D)  $\frac { 4 \sqrt { x + h } + \sqrt { x } } { h }$

Question 11

Find the sum or difference.
-$$\frac { 6 x ^ { 8 } + 30 x ^ { 5 } } { 3 x ^ { 2 } }$$

Accepted Answer

A)  $6 x ^ { 8 } + 10 x ^ { 3 }$ 
B)  $2 x ^ { 6 } + 30 x ^ { 5 }$ 
C)  $12 x ^ { 11 }$ 
D)  $2 x ^ { 6 } + 10 x ^ { 3 }$ 
A)  $6 x ^ { 8 } + 10 x ^ { 3 }$ 
B)  $2 x ^ { 6 } + 30 x ^ { 5 }$ 
C)  $12 x ^ { 11 }$ 
D)  $2 x ^ { 6 } + 10 x ^ { 3 }$

Question 12

Factor the trinomial, if possible.
-$7 x ^ { 2 } - 15 x y - 18 y ^ { 2 }$

Accepted Answer

A)  $( 7 x + 3 y ) ( x - 6 y )$ 
B)  $y ( 7 x + 6 ) ( x - 3 )$ 
C)  prime 
D)  $( 7 x + 6 y ) ( x - 3 y )$ 
A)  $( 7 x + 3 y ) ( x - 6 y )$ 
B)  $y ( 7 x + 6 ) ( x - 3 )$ 
C)  prime 
D)  $( 7 x + 6 y ) ( x - 3 y )$

Question 13

Factor the polynomial by substitution.
-$$60 z ^ { 8 } + 8 z ^ { 5 } - 32 z ^ { 2 }$$

Accepted Answer

A)  $4 \left( 3 z ^ { 6 } - 2 \right) \left( 5 z ^ { 2 } + 4 \right)$ 
B)  $\left( 3 z ^ { 4 } + 3 \right) \left( 5 z ^ { 4 } + 4 \right)$ 
C)  $4 z ^ { 2 } \left( 3 z ^ { 3 } - 2 \right) \left( 5 z ^ { 3 } + 4 \right)$ 
D)  $4 z ^ { 2 } \left( 5 z ^ { 3 } - 4 \right) \left( 3 z ^ { 3 } + 2 \right)$ 
A)  $4 \left( 3 z ^ { 6 } - 2 \right) \left( 5 z ^ { 2 } + 4 \right)$ 
B)  $\left( 3 z ^ { 4 } + 3 \right) \left( 5 z ^ { 4 } + 4 \right)$ 
C)  $4 z ^ { 2 } \left( 3 z ^ { 3 } - 2 \right) \left( 5 z ^ { 3 } + 4 \right)$ 
D)  $4 z ^ { 2 } \left( 5 z ^ { 3 } - 4 \right) \left( 3 z ^ { 3 } + 2 \right)$

Question 14

Simplify the expression. Assume all variables represent nonzero real numbers.
-$\left( x ^ { 4 } y ^ { 8 } \right) ^ { 3 }$

Accepted Answer

A)  $x ^ { 7 } y ^ { 11 }$ 
B)  $x ^ { 64 } y ^ { 512 }$ 
C)  $x ^ { 4 } y ^ { 24 }$ 
D)  $x ^ { 12 } y ^ { 24 }$ 
A)  $x ^ { 7 } y ^ { 11 }$ 
B)  $x ^ { 64 } y ^ { 512 }$ 
C)  $x ^ { 4 } y ^ { 24 }$ 
D)  $x ^ { 12 } y ^ { 24 }$

Question 15

Factor the trinomial, if possible.
-$14 x ^ { 2 } - 49 x - 28$

Accepted Answer

A)  $7 ( 2 x - 1 ) ( x + 4 )$ 
B)  $7 ( 2 x + 1 ) ( x - 4 )$ 
C)  $( 2 x - 1 ) ( 7 x + 28 )$ 
D)  $( 14 x - 7 ) ( x + 4 )$ 
A)  $7 ( 2 x - 1 ) ( x + 4 )$ 
B)  $7 ( 2 x + 1 ) ( x - 4 )$ 
C)  $( 2 x - 1 ) ( 7 x + 28 )$ 
D)  $( 14 x - 7 ) ( x + 4 )$

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$\frac { \sqrt { 98 } } { 5 } - \frac { 6 \sqrt { 2 } } { 5 } + \frac { \sqrt { 2 } } { \sqrt { 25 } }$

Accepted Answer

A)  $- \frac { \sqrt { 96 } } { 5 }$ 
B)  $\frac { 4 \sqrt { 2 } } { 5 }$ 
C)  $\frac { 2 \sqrt { 2 } } { 25 }$ 
D)  $\frac { 2 \sqrt { 2 } } { 5 }$ 
A)  $- \frac { \sqrt { 96 } } { 5 }$ 
B)  $\frac { 4 \sqrt { 2 } } { 5 }$ 
C)  $\frac { 2 \sqrt { 2 } } { 25 }$ 
D)  $\frac { 2 \sqrt { 2 } } { 5 }$

Question 17

Evaluate the expression.
-$- 4 \cdot 5 ^ { 2 }$

Accepted Answer

A)  $- 400$ 
B)  400 
C)  100 
D)  $- 100$ 
A)  $- 400$ 
B)  400 
C)  100 
D)  $- 100$

Question 18

Factor by any method.
-$$b ^ { 6 } - 64 z ^ { 6 }$$

Accepted Answer

A)  $( b + 2 z ) ( b - 2 z ) \left( b ^ { 2 } + 2 b z + 4 z ^ { 2 } \right) \left( b ^ { 2 } - 2 b z + 4 z ^ { 2 } \right)$ 
B)  $( b + 2 z ) ( b - 2 z ) \left( b ^ { 4 } + 4 b ^ { 2 } z ^ { 2 } + 16 z ^ { 4 } \right)$ 
C)  $\left( b ^ { 2 } - 4 z ^ { 2 } \right) \left( b ^ { 4 } + 4 b ^ { 2 } z ^ { 2 } + 16 z ^ { 4 } \right)$ 
D)  $\left( b ^ { 3 } + 8 z ^ { 3 } \right) \left( b ^ { 3 } - 8 z ^ { 3 } \right)$ 
A)  $( b + 2 z ) ( b - 2 z ) \left( b ^ { 2 } + 2 b z + 4 z ^ { 2 } \right) \left( b ^ { 2 } - 2 b z + 4 z ^ { 2 } \right)$ 
B)  $( b + 2 z ) ( b - 2 z ) \left( b ^ { 4 } + 4 b ^ { 2 } z ^ { 2 } + 16 z ^ { 4 } \right)$ 
C)  $\left( b ^ { 2 } - 4 z ^ { 2 } \right) \left( b ^ { 4 } + 4 b ^ { 2 } z ^ { 2 } + 16 z ^ { 4 } \right)$ 
D)  $\left( b ^ { 3 } + 8 z ^ { 3 } \right) \left( b ^ { 3 } - 8 z ^ { 3 } \right)$

Question 19

Simplify the expression. Assume all variables represent positive real numbers.
-$$\frac { \sqrt { 252 } } { 7 } - \frac { 2 \sqrt { 7 } } { 7 } + \frac { \sqrt { 7 } } { \sqrt { 49 } }$$

Accepted Answer

A)  $\frac { 7 \sqrt { 7 } } { 7 }$ 
B)  $\frac { 5 \sqrt { 7 } } { 49 }$ 
C)  $- \frac { \sqrt { 245 } } { 7 }$ 
D)  $\frac { 5 \sqrt { 7 } } { 7 }$ 
A)  $\frac { 7 \sqrt { 7 } } { 7 }$ 
B)  $\frac { 5 \sqrt { 7 } } { 49 }$ 
C)  $- \frac { \sqrt { 245 } } { 7 }$ 
D)  $\frac { 5 \sqrt { 7 } } { 7 }$

Question 20

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers.
-$5 x ^ { 0 }$

Accepted Answer

A)  1 
B)  0 
C)  $x$ 
D)  5 
A)  1 
B)  0 
C)  $x$ 
D)  5

Factor the trinomial, if possible. - $( m - 3 n ) ^ { 2 } - 8 ( m - 3 n ) + 16$

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

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -Find the magnitude of the difference between a windchill factor of $- 50$ and a windchill factor of $- 5$ .

Find the product or quotient. - $\frac { ( x - y ) ^ { 2 } - 49 } { ( x + y ) ^ { 2 } - 49 } + \frac { x - y - 7 } { x + y + 7 }$

Tell whether the statement is true or false. - $\{ 5,7,8,10 \} \cap \varnothing = \{ 5,7,8,10 \}$

Factor by any method. - $15 x ^ { 10 } + 18 x ^ { 5 } y ^ { 4 } + 20 x ^ { 5 } y ^ { 4 } + 24 y ^ { 8 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 18 y ^ { 3 } + 6 y ^ { 2 } + - 5$

Find the sum or difference. - $\left( 4 a ^ { 4 } - 7 a ^ { 2 } \right) + \left( 8 a ^ { 4 } - 3 a ^ { 2 } \right)$

Identify the property illustrated by the statement. Assume all variables represent real numbers. - $6 ( \pi ) \text { is a real number. }$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - $\frac { 4 } { \sqrt { x + h } - \sqrt { x } }$

Find the sum or difference. - $\frac { 6 x ^ { 8 } + 30 x ^ { 5 } } { 3 x ^ { 2 } }$

Factor the trinomial, if possible. - $7 x ^ { 2 } - 15 x y - 18 y ^ { 2 }$

Factor the polynomial by substitution. - $60 z ^ { 8 } + 8 z ^ { 5 } - 32 z ^ { 2 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( x ^ { 4 } y ^ { 8 } \right) ^ { 3 }$

Factor the trinomial, if possible. - $14 x ^ { 2 } - 49 x - 28$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 98 } } { 5 } - \frac { 6 \sqrt { 2 } } { 5 } + \frac { \sqrt { 2 } } { \sqrt { 25 } }$

Evaluate the expression. - $- 4 \cdot 5 ^ { 2 }$

Factor by any method. - $b ^ { 6 } - 64 z ^ { 6 }$

Simplify the expression. Assume all variables represent positive real numbers. - $\frac { \sqrt { 252 } } { 7 } - \frac { 2 \sqrt { 7 } } { 7 } + \frac { \sqrt { 7 } } { \sqrt { 49 } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $5 x ^ { 0 }$

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Exam 1: Review of Basic Concepts

Factor the trinomial, if possible. - (m−3n)2−8(m−3n)+16( m - 3 n ) ^ { 2 } - 8 ( m - 3 n ) + 16(m−3n)2−8(m−3n)+16

Determine what signs on values of x and y would make the statement true. Assume that x and y are not 0. -Find the magnitude of the difference between a windchill factor of −50- 50−50 and a windchill factor of −5- 5−5 .

Find the product or quotient. - (x−y)2−49(x+y)2−49+x−y−7x+y+7\frac { ( x - y ) ^ { 2 } - 49 } { ( x + y ) ^ { 2 } - 49 } + \frac { x - y - 7 } { x + y + 7 }(x+y)2−49(x−y)2−49​+x+y+7x−y−7​

Tell whether the statement is true or false. - {5,7,8,10}∩∅={5,7,8,10}\{ 5,7,8,10 \} \cap \varnothing = \{ 5,7,8,10 \}{5,7,8,10}∩∅={5,7,8,10}

Factor by any method. - 15x10+18x5y4+20x5y4+24y815 x ^ { 10 } + 18 x ^ { 5 } y ^ { 4 } + 20 x ^ { 5 } y ^ { 4 } + 24 y ^ { 8 }15x10+18x5y4+20x5y4+24y8

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −18y3+6y2+−5- 18 y ^ { 3 } + 6 y ^ { 2 } + - 5−18y3+6y2+−5

Find the sum or difference. - (4a4−7a2)+(8a4−3a2)\left( 4 a ^ { 4 } - 7 a ^ { 2 } \right) + \left( 8 a ^ { 4 } - 3 a ^ { 2 } \right)(4a4−7a2)+(8a4−3a2)

Identify the property illustrated by the statement. Assume all variables represent real numbers. - 6(π) is a real number. 6 ( \pi ) \text { is a real number. }6(π) is a real number.

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. - 4x+h−x\frac { 4 } { \sqrt { x + h } - \sqrt { x } }x+h​−x​4​

Find the sum or difference. - 6x8+30x53x2\frac { 6 x ^ { 8 } + 30 x ^ { 5 } } { 3 x ^ { 2 } }3x26x8+30x5​

Factor the trinomial, if possible. - 7x2−15xy−18y27 x ^ { 2 } - 15 x y - 18 y ^ { 2 }7x2−15xy−18y2

Factor the polynomial by substitution. - 60z8+8z5−32z260 z ^ { 8 } + 8 z ^ { 5 } - 32 z ^ { 2 }60z8+8z5−32z2

Simplify the expression. Assume all variables represent nonzero real numbers. - (x4y8)3\left( x ^ { 4 } y ^ { 8 } \right) ^ { 3 }(x4y8)3

Factor the trinomial, if possible. - 14x2−49x−2814 x ^ { 2 } - 49 x - 2814x2−49x−28

Simplify the expression. Assume all variables represent positive real numbers. - 985−625+225\frac { \sqrt { 98 } } { 5 } - \frac { 6 \sqrt { 2 } } { 5 } + \frac { \sqrt { 2 } } { \sqrt { 25 } }598​​−562​​+25​2​​

Evaluate the expression. - −4⋅52- 4 \cdot 5 ^ { 2 }−4⋅52

Factor by any method. - b6−64z6b ^ { 6 } - 64 z ^ { 6 }b6−64z6

Simplify the expression. Assume all variables represent positive real numbers. - 2527−277+749\frac { \sqrt { 252 } } { 7 } - \frac { 2 \sqrt { 7 } } { 7 } + \frac { \sqrt { 7 } } { \sqrt { 49 } }7252​​−727​​+49​7​​

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 5x05 x ^ { 0 }5x0