Question 1

Find the product.
-$$( x - 11 y ) ( x + 2 y )$$

Accepted Answer

A)  $x ^ { 2 } - 12 x y - 22 y ^ { 2 }$ 
B)  $x - 9 x y - 22 y$ 
C)  $x ^ { 2 } - 9 x y - 9 y ^ { 2 }$ 
D)  $x ^ { 2 } - 9 x y - 22 y ^ { 2 }$ 
A)  $x ^ { 2 } - 12 x y - 22 y ^ { 2 }$ 
B)  $x - 9 x y - 22 y$ 
C)  $x ^ { 2 } - 9 x y - 9 y ^ { 2 }$ 
D)  $x ^ { 2 } - 9 x y - 22 y ^ { 2 }$

Question 2

Factor, using the given factor. Assume all variables represent positive real numbers.
-$2 ( 5 x - 1 ) ^ { - 3 / 4 } + 4 ( 5 x - 1 ) ^ { 1 / 4 } + 8 ( 5 x - 1 ) ^ { 5 / 4 } ; \quad 2 ( 5 x - 1 ) ^ { - 3 / 4 }$

Accepted Answer

A)  $2 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 100 x ^ { 2 } - 30 x - 3 \right)$ 
B)  $4 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 25 x ^ { 2 } - 15 x + 1 \right)$ 
C)  $4 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 25 x ^ { 2 } - 15 x - 1 \right)$ 
D)  $2 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 100 x ^ { 2 } - 30 x + 3 \right)$ 
A)  $2 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 100 x ^ { 2 } - 30 x - 3 \right)$ 
B)  $4 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 25 x ^ { 2 } - 15 x + 1 \right)$ 
C)  $4 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 25 x ^ { 2 } - 15 x - 1 \right)$ 
D)  $2 ( 5 x - 1 ) ^ { - 3 / 4 } \left( 100 x ^ { 2 } - 30 x + 3 \right)$

Question 3

Evaluate the expression for x = -2, y = 3, and a = -4.
-$$\frac { \frac { 9 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 12 } { y } }$$

Accepted Answer

A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  2 
D)  $\frac { 5 } { 4 }$ 
A)  $\frac { 5 } { 3 }$ 
B)  $\frac { 1 } { 3 }$ 
C)  2 
D)  $\frac { 5 } { 4 }$

Question 4

Factor the polynomial by substitution.
-$15 z ^ { 6 } + 4 z ^ { 3 } - 4$

Accepted Answer

A)  $\left( 3 z ^ { 3 } + 2 \right) \left( 5 z ^ { 3 } - 2 \right)$ 
B)  $\left( 3 z ^ { 3 } + 1 \right) \left( 5 z ^ { 3 } - 4 \right)$ 
C)  $\left( 5 z ^ { 3 } + 2 \right) \left( 3 z ^ { 3 } - 2 \right)$ 
D)  $15 \left( z ^ { 3 } - 2 \right) \left( z ^ { 3 } + 2 \right)$ 
A)  $\left( 3 z ^ { 3 } + 2 \right) \left( 5 z ^ { 3 } - 2 \right)$ 
B)  $\left( 3 z ^ { 3 } + 1 \right) \left( 5 z ^ { 3 } - 4 \right)$ 
C)  $\left( 5 z ^ { 3 } + 2 \right) \left( 3 z ^ { 3 } - 2 \right)$ 
D)  $15 \left( z ^ { 3 } - 2 \right) \left( z ^ { 3 } + 2 \right)$

Question 5

Divide.
-$\frac { 16 s t ^ { 4 } - 5 t ^ { 6 } + 64 s t ^ { 3 } } { 4 s t ^ { 3 } }$

Accepted Answer

A)  $4 s t - \frac { 5 t ^ { 3 } } { 4 s } + 16$ 
B)  $4 \mathrm { t } - \mathrm { st } ^ { 3 } + 16$ 
C)  $4 t - \frac { 5 t ^ { 3 } } { 4 s } + 16$ 
D)  $4 t - \frac { t ^ { 3 } } { s } + 16$ 
A)  $4 s t - \frac { 5 t ^ { 3 } } { 4 s } + 16$ 
B)  $4 \mathrm { t } - \mathrm { st } ^ { 3 } + 16$ 
C)  $4 t - \frac { 5 t ^ { 3 } } { 4 s } + 16$ 
D)  $4 t - \frac { t ^ { 3 } } { s } + 16$

Question 6

Find the sum or difference.
-$$\left( 4 x ^ { 9 } + 11 x ^ { 7 } - 9 x ^ { 2 } + 12 \right) - \left( 6 x ^ { 9 } - 3 x ^ { 5 } + 3 x ^ { 2 } - 12 \right)$$

Accepted Answer

A)  $- 2 x ^ { 9 } + 11 x ^ { 7 } - 3 x ^ { 5 } - 12 x ^ { 2 } + 24$ 
B)  $2 x ^ { 9 } + 11 x ^ { 7 } + 3 x ^ { 5 } - 12 x ^ { 2 } + 24$ 
C)  $- 2 x ^ { 9 } + 11 x ^ { 7 } + 3 x ^ { 5 } - 12 x ^ { 2 } + 24$ 
D)  $2 x ^ { 9 } + 11 x ^ { 7 } - 3 x ^ { 5 } - 12 x ^ { 2 } + 24$ 
A)  $- 2 x ^ { 9 } + 11 x ^ { 7 } - 3 x ^ { 5 } - 12 x ^ { 2 } + 24$ 
B)  $2 x ^ { 9 } + 11 x ^ { 7 } + 3 x ^ { 5 } - 12 x ^ { 2 } + 24$ 
C)  $- 2 x ^ { 9 } + 11 x ^ { 7 } + 3 x ^ { 5 } - 12 x ^ { 2 } + 24$ 
D)  $2 x ^ { 9 } + 11 x ^ { 7 } - 3 x ^ { 5 } - 12 x ^ { 2 } + 24$

Question 7

Decide whether the expression has been simplified correctly.
-$$2 ^ { 0 } \mathrm { x } = 1$$

Accepted Answer

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

Question 8

Find the product.
-$$( 5 y - 8 ) \left( 25 y ^ { 2 } + 40 y + 64 \right)$$

Accepted Answer

A)  $125 y ^ { 3 } + 320 y ^ { 2 } - 512$ 
B)  $125 y ^ { 3 } + 512$ 
C)  $125 y ^ { 3 } - 512$ 
D)  $25 y ^ { 3 } + 512$ 
A)  $125 y ^ { 3 } + 320 y ^ { 2 } - 512$ 
B)  $125 y ^ { 3 } + 512$ 
C)  $125 y ^ { 3 } - 512$ 
D)  $25 y ^ { 3 } + 512$

Question 9

Perform the indicated operations.
-$$\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + \frac { 4 } { 2 }$$

Accepted Answer

A)  $\frac { 2 a + 3 b } { a + b }$ 
B)  $\frac { 2 a + 3 b } { a ^ { 2 } - b ^ { 2 } }$ 
C)  $\frac { 2 a b - b + 2 } { a + b + 1 }$ 
D)  $\frac { ( a - b ) ( 2 a + 3 b ) } { a ^ { 2 } - b ^ { 2 } }$ 
A)  $\frac { 2 a + 3 b } { a + b }$ 
B)  $\frac { 2 a + 3 b } { a ^ { 2 } - b ^ { 2 } }$ 
C)  $\frac { 2 a b - b + 2 } { a + b + 1 }$ 
D)  $\frac { ( a - b ) ( 2 a + 3 b ) } { a ^ { 2 } - b ^ { 2 } }$

Question 10

Perform the indicated operation and write your answer with positive integer exponents.
-$\frac { m ^ { - 1 } - n ^ { - 1 } } { ( m n ) ^ { - 1 } }$

Accepted Answer

A)  $n - m$ 
B)  $m - n$ 
C)  $- \mathrm { n } - \mathrm { m }$ 
D)  $m + n$ m 
A)  $n - m$ 
B)  $m - n$ 
C)  $- \mathrm { n } - \mathrm { m }$ 
D)  $m + n$ m

Question 11

Simplify the expression. Assume all variables represent positive real numbers.
-$\sqrt [ 5 ] { \mathrm { x } ^ { 19 } \mathrm { y } ^ { 7 } \mathrm { z } ^ { 13 } }$

Accepted Answer

A)  $x y z \sqrt [ 5 ] { x ^ { 4 } y ^ { 2 } z ^ { 3 } }$ 
B)  $x ^ { 15 } y ^ { 5 } z ^ { 10 } \sqrt [ 5 ] { x ^ { 4 } y ^ { 2 } z ^ { 3 } }$ 
C)  $x ^ { 3 } y z ^ { 2 } \sqrt [ 5 ] { x ^ { 4 } y ^ { 2 } z ^ { 3 } }$ 
D)  $x ^ { 3 } y ^ { 2 } \sqrt [ 5 ] { y ^ { 2 } z ^ { 3 } }$ 
A)  $x y z \sqrt [ 5 ] { x ^ { 4 } y ^ { 2 } z ^ { 3 } }$ 
B)  $x ^ { 15 } y ^ { 5 } z ^ { 10 } \sqrt [ 5 ] { x ^ { 4 } y ^ { 2 } z ^ { 3 } }$ 
C)  $x ^ { 3 } y z ^ { 2 } \sqrt [ 5 ] { x ^ { 4 } y ^ { 2 } z ^ { 3 } }$ 
D)  $x ^ { 3 } y ^ { 2 } \sqrt [ 5 ] { y ^ { 2 } z ^ { 3 } }$

Question 12

Simplify the expression. Assume all variables represent positive real numbers.
-$( \sqrt { 6 } - 7 ) ( \sqrt { 7 } + 3 )$

Accepted Answer

A)  $\sqrt { 42 } - 4 \sqrt { 7 } - 21$ 
B)  $- 3 \sqrt { 42 } - 21$ 
C)  $\sqrt { 42 } - 21$ 
D)  $\sqrt { 42 } + 3 \sqrt { 6 } - 7 \sqrt { 7 } - 21$ 
A)  $\sqrt { 42 } - 4 \sqrt { 7 } - 21$ 
B)  $- 3 \sqrt { 42 } - 21$ 
C)  $\sqrt { 42 } - 21$ 
D)  $\sqrt { 42 } + 3 \sqrt { 6 } - 7 \sqrt { 7 } - 21$

Question 13

Find the product or quotient.
-$\frac { 8 x ^ { 2 } } { 2 } \cdot \frac { 12 } { x ^ { 3 } }$

Accepted Answer

A)  $\frac { 48 } { x ^ { 2 } }$ 
B)  $48 x$ 
C)  $\frac { 96 } { x }$ 
D)  $\frac { 48 } { x }$ 
A)  $\frac { 48 } { x ^ { 2 } }$ 
B)  $48 x$ 
C)  $\frac { 96 } { x }$ 
D)  $\frac { 48 } { x }$

Question 14

Factor the trinomial, if possible.
-$98 m ^ { 2 } - 140 m n + 50 n ^ { 2 }$

Accepted Answer

A)  $( 14 m + 5 n ) ^ { 2 }$ 
B)  $( 14 \mathrm {~m} - 10 \mathrm { n } ) ^ { 2 }$ 
C)  $2 ( 7 m + 5 n ) ^ { 2 }$ 
D)  $2 ( 7 m - 5 n ) ^ { 2 }$ 
A)  $( 14 m + 5 n ) ^ { 2 }$ 
B)  $( 14 \mathrm {~m} - 10 \mathrm { n } ) ^ { 2 }$ 
C)  $2 ( 7 m + 5 n ) ^ { 2 }$ 
D)  $2 ( 7 m - 5 n ) ^ { 2 }$

Question 15

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true.
-11_______ $\{ 7,10,13,11,9 \}$

Accepted Answer

A)    
B)    
A)    
B)

Question 16

Divide.
-$$\frac { x ^ { 2 } - 10 x + 24 } { x - 4 }$$

Accepted Answer

A)  $x + 4$ 
B)  $x - 6$ 
C)  $x + 6$ 
D)  $6 - \mathrm { x }$ 
A)  $x + 4$ 
B)  $x - 6$ 
C)  $x + 6$ 
D)  $6 - \mathrm { x }$

Question 17

Evaluate the expression.
-Let $x = 6$ and $y = - 2$. Evaluate $\frac { | x | } { x } + \frac { | y | } { y }$.

Accepted Answer

A)  $- 1$ 
B)  0 
C)  1 
D)  2 
A)  $- 1$ 
B)  0 
C)  1 
D)  2

Question 18

Decide whether the statement is true or false. If false, correct the statement so it is true.
-$$| - 5 | = | 5 |$$

Accepted Answer

A)  True 
B)  False; $| - 5 | = - | 5 | = - 5$ 
A)  True 
B)  False; $| - 5 | = - | 5 | = - 5$

Question 19

Tell whether the statement is true or false.
-Let $\mathrm { A } = \{ 3,4,5,6,7,8 \} , \mathrm { B } = \{ 5,7,9 \} , \mathrm { C } = \{ 3,4,6,8 \} , \mathrm { D } = \{ 3,8 \}$, and $\mathrm { U } = \{ 3,4,5,6,7,8,9 \}$.
$\{ 7,9 \} \subseteq \mathrm { B }$

Accepted Answer

A)  True 
B)  False 
A)  True 
B)  False

Question 20

Evaluate the expression.
-$3125 ^ { 4 / 5 }$

Accepted Answer

A)  390,625 
B)  78,125 
C)  625 
D)  $1,953,125$ 
A)  390,625 
B)  78,125 
C)  625 
D)  $1,953,125$

Find the product. - $( x - 11 y ) ( x + 2 y )$

Factor, using the given factor. Assume all variables represent positive real numbers. - $2 ( 5 x - 1 ) ^ { - 3 / 4 } + 4 ( 5 x - 1 ) ^ { 1 / 4 } + 8 ( 5 x - 1 ) ^ { 5 / 4 } ; \quad 2 ( 5 x - 1 ) ^ { - 3 / 4 }$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { \frac { 9 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 12 } { y } }$

Factor the polynomial by substitution. - $15 z ^ { 6 } + 4 z ^ { 3 } - 4$

Divide. - $\frac { 16 s t ^ { 4 } - 5 t ^ { 6 } + 64 s t ^ { 3 } } { 4 s t ^ { 3 } }$

Find the sum or difference. - $\left( 4 x ^ { 9 } + 11 x ^ { 7 } - 9 x ^ { 2 } + 12 \right) - \left( 6 x ^ { 9 } - 3 x ^ { 5 } + 3 x ^ { 2 } - 12 \right)$

Decide whether the expression has been simplified correctly. - $2 ^ { 0 } \mathrm { x } = 1$

Find the product. - $( 5 y - 8 ) \left( 25 y ^ { 2 } + 40 y + 64 \right)$

Perform the indicated operations. - $\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + \frac { 4 } { 2 }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { m ^ { - 1 } - n ^ { - 1 } } { ( m n ) ^ { - 1 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 5 ] { \mathrm { x } ^ { 19 } \mathrm { y } ^ { 7 } \mathrm { z } ^ { 13 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $( \sqrt { 6 } - 7 ) ( \sqrt { 7 } + 3 )$

Find the product or quotient. - $\frac { 8 x ^ { 2 } } { 2 } \cdot \frac { 12 } { x ^ { 3 } }$

Factor the trinomial, if possible. - $98 m ^ { 2 } - 140 m n + 50 n ^ { 2 }$

Insert $\in \mathbf { Or } \notin$ in the blank to make the statement is true. -11_______ $\{ 7,10,13,11,9 \}$

Divide. - $\frac { x ^ { 2 } - 10 x + 24 } { x - 4 }$

Evaluate the expression. -Let $x = 6$ and $y = - 2$ . Evaluate $\frac { | x | } { x } + \frac { | y | } { y }$ .

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 5 | = | 5 |$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 3,4,5,6,7,8 \} , \mathrm { B } = \{ 5,7,9 \} , \mathrm { C } = \{ 3,4,6,8 \} , \mathrm { D } = \{ 3,8 \}$ , and $\mathrm { U } = \{ 3,4,5,6,7,8,9 \}$ . $\{ 7,9 \} \subseteq \mathrm { B }$

Evaluate the expression. - $3125 ^ { 4 / 5 }$

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Exam 12: Review of Basic Concepts

Find the product. - (x−11y)(x+2y)( x - 11 y ) ( x + 2 y )(x−11y)(x+2y)

Evaluate the expression for x = -2, y = 3, and a = -4. - 9y−a2x2+12y\frac { \frac { 9 } { y } - \frac { a } { 2 } } { \frac { x } { 2 } + \frac { 12 } { y } }2x​+y12​y9​−2a​​

Factor the polynomial by substitution. - 15z6+4z3−415 z ^ { 6 } + 4 z ^ { 3 } - 415z6+4z3−4

Divide. - 16st4−5t6+64st34st3\frac { 16 s t ^ { 4 } - 5 t ^ { 6 } + 64 s t ^ { 3 } } { 4 s t ^ { 3 } }4st316st4−5t6+64st3​

Find the sum or difference. - (4x9+11x7−9x2+12)−(6x9−3x5+3x2−12)\left( 4 x ^ { 9 } + 11 x ^ { 7 } - 9 x ^ { 2 } + 12 \right) - \left( 6 x ^ { 9 } - 3 x ^ { 5 } + 3 x ^ { 2 } - 12 \right)(4x9+11x7−9x2+12)−(6x9−3x5+3x2−12)

Decide whether the expression has been simplified correctly. - 20x=12 ^ { 0 } \mathrm { x } = 120x=1

Find the product. - (5y−8)(25y2+40y+64)( 5 y - 8 ) \left( 25 y ^ { 2 } + 40 y + 64 \right)(5y−8)(25y2+40y+64)

Perform the indicated operations. - 2aba2−b2−ba−b+42\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + \frac { 4 } { 2 }a2−b22ab​−a−bb​+24​

Perform the indicated operation and write your answer with positive integer exponents. - m−1−n−1(mn)−1\frac { m ^ { - 1 } - n ^ { - 1 } } { ( m n ) ^ { - 1 } }(mn)−1m−1−n−1​

Simplify the expression. Assume all variables represent positive real numbers. - x19y7z135\sqrt [ 5 ] { \mathrm { x } ^ { 19 } \mathrm { y } ^ { 7 } \mathrm { z } ^ { 13 } }5x19y7z13​

Simplify the expression. Assume all variables represent positive real numbers. - (6−7)(7+3)( \sqrt { 6 } - 7 ) ( \sqrt { 7 } + 3 )(6​−7)(7​+3)

Find the product or quotient. - 8x22⋅12x3\frac { 8 x ^ { 2 } } { 2 } \cdot \frac { 12 } { x ^ { 3 } }28x2​⋅x312​

Factor the trinomial, if possible. - 98m2−140mn+50n298 m ^ { 2 } - 140 m n + 50 n ^ { 2 }98m2−140mn+50n2

Insert ∈Or∉\in \mathbf { Or } \notin∈Or∈/ in the blank to make the statement is true. -11_______ {7,10,13,11,9}\{ 7,10,13,11,9 \}{7,10,13,11,9}

Divide. - x2−10x+24x−4\frac { x ^ { 2 } - 10 x + 24 } { x - 4 }x−4x2−10x+24​

Evaluate the expression. -Let x=6x = 6x=6 and y=−2y = - 2y=−2 . Evaluate ∣x∣x+∣y∣y\frac { | x | } { x } + \frac { | y | } { y }x∣x∣​+y∣y∣​ .

Decide whether the statement is true or false. If false, correct the statement so it is true. - ∣−5∣=∣5∣| - 5 | = | 5 |∣−5∣=∣5∣

Evaluate the expression. - 31254/53125 ^ { 4 / 5 }31254/5