Question 1

Factor out the greatest common factor. Simplify the factors, if possible.
-$12 w x - 9 w y - 15 w z$

Accepted Answer

A)  $3 w ( 4 x - 3 y - 5 z )$ 
B)  $12 w ( x - 9 y - 15 z )$ 
C)  $3 ( 4 w x - 3 w y - 5 w z )$ 
D)  $3 w ( 4 x - 9 w y - 15 w z )$ 
A)  $3 w ( 4 x - 3 y - 5 z )$ 
B)  $12 w ( x - 9 y - 15 z )$ 
C)  $3 ( 4 w x - 3 w y - 5 w z )$ 
D)  $3 w ( 4 x - 9 w y - 15 w z )$

Question 2

Factor by any method.
-$b ^ { 6 } - 1$

Accepted Answer

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

Question 3

Find the product.
-$$( p + 15 ) ^ { 2 }$$

Accepted Answer

A)  $p ^ { 2 } + 30 p + 225$ 
B)  $p + 225$ 
C)  $p ^ { 2 } + 225$ 
D)  $225 p ^ { 2 } + 30 p + 225$ 
A)  $p ^ { 2 } + 30 p + 225$ 
B)  $p + 225$ 
C)  $p ^ { 2 } + 225$ 
D)  $225 p ^ { 2 } + 30 p + 225$

Question 4

Find the product.
-$- 5 a ^ { 3 } x ^ { 6 } \left( - 5 a ^ { 7 } x ^ { 8 } + 2 x ^ { 6 } + 4 a \right)$

Accepted Answer

A)  $25 a ^ { 21 } x ^ { 48 } + 10 a ^ { 3 } x ^ { 36 } + 20 a ^ { 3 } x ^ { 6 }$ 
B)  $- 25 a ^ { 10 } x^{ 14} + 10 a ^ { 3 } x^{ 12 }+ 20 a ^ { 4 } x ^ { 6 }$ 
C)  $25 a 10x^{ 14} - 10 a ^ { 3 } { x } ^{12} - 20 a ^ { 4 } x ^ { 6 }$ 
D)  $25 a 10x^{14} + 2 x ^ { 6 } + 4 a$ 
A)  $25 a ^ { 21 } x ^ { 48 } + 10 a ^ { 3 } x ^ { 36 } + 20 a ^ { 3 } x ^ { 6 }$ 
B)  $- 25 a ^ { 10 } x^{ 14} + 10 a ^ { 3 } x^{ 12 }+ 20 a ^ { 4 } x ^ { 6 }$ 
C)  $25 a 10x^{ 14} - 10 a ^ { 3 } { x } ^{12} - 20 a ^ { 4 } x ^ { 6 }$ 
D)  $25 a 10x^{14} + 2 x ^ { 6 } + 4 a$

Question 5

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

Accepted Answer

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

Question 6

Factor by any method.
-$8 p ^ { 3 } - 1$

Accepted Answer

A)  $( 2 p + 1 ) \left( 4 p ^ { 2 } - 2 p + 1 \right)$ 
B)  $( 8 p - 1 ) \left( p ^ { 2 } + 2 p + 1 \right)$ 
C)  $( 2 p - 1 ) \left( 4 p ^ { 2 } + 1 \right)$ 
D)  $( 2 p - 1 ) \left( 4 p ^ { 2 } + 2 p + 1 \right)$ 
A)  $( 2 p + 1 ) \left( 4 p ^ { 2 } - 2 p + 1 \right)$ 
B)  $( 8 p - 1 ) \left( p ^ { 2 } + 2 p + 1 \right)$ 
C)  $( 2 p - 1 ) \left( 4 p ^ { 2 } + 1 \right)$ 
D)  $( 2 p - 1 ) \left( 4 p ^ { 2 } + 2 p + 1 \right)$

Question 7

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

Accepted Answer

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

Question 8

Use these sets to find the following. Identify any disjoint sets.
-Let $\mathrm { U } = \{ 7,8,9,10,11,12,13,14,15,16,17 \} , \mathrm { M } = \{ 7,9,11,13 \} , \mathrm { N } = \{ 8,10,12,14,16 \}$, $Q = \{ 7,9,11,13,15,17 \}$, and $R = \{ 7,8,9,10 \}$.
$\mathrm { M } \cup \mathrm { N }$

Accepted Answer

A)  $\{ 8,9,10,11,12,13,14,15,16 \}$ 
B)  $\{ 7,8,9,10,11,12,16 \}$ 
C)  $\{ 7,8,9,10,11,12,13,14,16 \}$ 
D)  $\varnothing ; \mathrm { M }$ and $\mathrm { N }$ are disjoint sets. 
A)  $\{ 8,9,10,11,12,13,14,15,16 \}$ 
B)  $\{ 7,8,9,10,11,12,16 \}$ 
C)  $\{ 7,8,9,10,11,12,13,14,16 \}$ 
D)  $\varnothing ; \mathrm { M }$ and $\mathrm { N }$ are disjoint sets.

Question 9

Simplify the expression. Assume all variables represent positive real numbers.
-$$4 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$$

Accepted Answer

A)  $4 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$ 
B)  $12 \sqrt [ 3 ] { a }$ 
C)  $5 \sqrt [ 3 ] { 27 a }$ 
D)  $7 \sqrt [ 3 ] { \mathrm { a } }$ 
A)  $4 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$ 
B)  $12 \sqrt [ 3 ] { a }$ 
C)  $5 \sqrt [ 3 ] { 27 a }$ 
D)  $7 \sqrt [ 3 ] { \mathrm { a } }$

Question 10

Provide an appropriate response.
-The formula used to find the volume of the frustum of a square pyramid is $V = \frac { 1 } { 3 } h \left( a ^ { 2 } + a b + b ^ { 2 } \right)$, where $b$ is the length of the base, $a$ is the length of the top, and $h$ is the height. Try to visualize the figure if $a = b = h$. Calculate the volume if $a = 261$ feet, $b = 261$ feet, and $h = 261$ feet.

Accepted Answer

A)  $17,779,681$ cubic feet 
B)  $17,779,581$ cubic feet 
C)  68,121 cubic feet 
D)  $17,780,581$ cubic feet 
A)  $17,779,681$ cubic feet 
B)  $17,779,581$ cubic feet 
C)  68,121 cubic feet 
D)  $17,780,581$ cubic feet

Question 11

Divide.
-$\frac { - 9 x ^ { 7 } - 9 x ^ { 6 } - 12 x ^ { 5 } } { - 3 x ^ { 6 } }$

Accepted Answer

A)  $3 x - 9 x ^ { 6 } + \frac { 4 } { x }$ 
B)  $7 x + 3$ 
C)  $3 x + 3 + \frac { 4 } { x }$ 
D)  $3 x + 3$ 
A)  $3 x - 9 x ^ { 6 } + \frac { 4 } { x }$ 
B)  $7 x + 3$ 
C)  $3 x + 3 + \frac { 4 } { x }$ 
D)  $3 x + 3$

Question 12

Evaluate the expression.
-$$( - 6 ) ^ { 3 } - ( - 6 ) ^ { 2 }$$

Accepted Answer

A)  $- 252$ 
B)  $- 180$ 
C)  180 
D)  252 
A)  $- 252$ 
B)  $- 180$ 
C)  180 
D)  252

Question 13

Find the sum or difference.
-$$\left( 5 x ^ { 4 } + 3 x ^ { 6 } - 5 + 7 x ^ { 5 } \right) - \left( 7 - 3 x ^ { 5 } + 8 x ^ { 6 } + 9 x ^ { 4 } \right)$$

Accepted Answer

A)  $- 5 x ^ { 6 } + 10 x ^ { 5 } - 4 x ^ { 4 } - 12$ 
B)  $- 5 x ^ { 6 } + 4 x ^ { 5 } + 14 x ^ { 4 } + 2$ 
C)  $11 x ^ { 6 } + 4 x ^ { 5 } + 14 x ^ { 4 } - 12$ 
D)  $11 x ^ { 6 } + 4 x ^ { 5 } + 14 x ^ { 4 } + 2$ 
A)  $- 5 x ^ { 6 } + 10 x ^ { 5 } - 4 x ^ { 4 } - 12$ 
B)  $- 5 x ^ { 6 } + 4 x ^ { 5 } + 14 x ^ { 4 } + 2$ 
C)  $11 x ^ { 6 } + 4 x ^ { 5 } + 14 x ^ { 4 } - 12$ 
D)  $11 x ^ { 6 } + 4 x ^ { 5 } + 14 x ^ { 4 } + 2$

Question 14

Use set notation, and list all the elements of the set.
-$\{ 83,79,75 , \ldots , 43 \}$

Accepted Answer

A)  $\{ 83,79,75,71,67,63,59,55,51,47,43 \}$ 
B)  $\{ 83,79,75,70,66,62,58,54,50,46,42 \}$ 
C)  $\{ 83,87,91,95,99,103,107,111,115,119,123 \}$ 
D)  $\{ 83,79,75,67,59,51,43 \}$ 
A)  $\{ 83,79,75,71,67,63,59,55,51,47,43 \}$ 
B)  $\{ 83,79,75,70,66,62,58,54,50,46,42 \}$ 
C)  $\{ 83,87,91,95,99,103,107,111,115,119,123 \}$ 
D)  $\{ 83,79,75,67,59,51,43 \}$

Question 15

Divide.
-$\frac { 10 x ^ { 3 } + 5 x ^ { 2 } - 3 x - 1 } { - 2 x + 1 }$

Accepted Answer

A)  $x ^ { 2 } - 5 x - 1$ 
B)  $x ^ { 2 } + 5 x + 1$ 
C)  $- 5 x ^ { 2 } - 5 x - 1$ 
D)  $- 5 x ^ { 2 } - 1$ 
A)  $x ^ { 2 } - 5 x - 1$ 
B)  $x ^ { 2 } + 5 x + 1$ 
C)  $- 5 x ^ { 2 } - 5 x - 1$ 
D)  $- 5 x ^ { 2 } - 1$

Question 16

Simplify the expression. Assume all variables represent positive real numbers.
-$$6 \sqrt [ 3 ] { 3 } + 11 \sqrt [ 3 ] { 3 }$$

Accepted Answer

A)  $17 \sqrt [ 3 ] { 6 }$ 
B)  $17 \sqrt [ 3 ] { 9 }$ 
C)  $5 \sqrt [ 3 ] { 3 }$ 
D)  $17 \sqrt [ 3 ] { 3 }$ 
A)  $17 \sqrt [ 3 ] { 6 }$ 
B)  $17 \sqrt [ 3 ] { 9 }$ 
C)  $5 \sqrt [ 3 ] { 3 }$ 
D)  $17 \sqrt [ 3 ] { 3 }$

Question 17

Identify the polynomial as a monomial, binomial, trinomial, or none of these.
-$- 11 x ^ { 3 } - 6 w ^ { 2 } - 6 w - 5 y ^ { 4 } - 2$

Accepted Answer

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

Question 18

Identify the set as finite or infinite.
-$\{ 8,16,24 , \ldots , 48 \}$

Accepted Answer

A)  infinite 
B)  finite 
A)  infinite 
B)  finite

Question 19

Find the product.
-$$( - 8 x - 9 ) ^ { 2 }$$

Accepted Answer

A)  $- 8 x ^ { 2 } + 144 x + 81$ 
B)  $64 x ^ { 2 } + 81$ 
C)  $64 x ^ { 2 } + 144 x + 81$ 
D)  $- 8 x ^ { 2 } + 81$ 
A)  $- 8 x ^ { 2 } + 144 x + 81$ 
B)  $64 x ^ { 2 } + 81$ 
C)  $64 x ^ { 2 } + 144 x + 81$ 
D)  $- 8 x ^ { 2 } + 81$

Question 20

Solve the problem.
-When determining appropriate doses of medication, it is sometimes important to estimate the body surface area (BSA) of a patient. This surface area (in $\mathrm { m } ^ { 2 }$ ) can be approximated using the Mosteller formula BSA $= \left( \frac { h \cdot w } { 3600 } \right) ^ { 1 / 2 }$, where $h$ is the patient's height in centimeters and $w$ is the weight in kilograms. Determine the BSA for a patient with height $174 \mathrm {~cm}$ and weight $55 \mathrm {~kg}$. Round your answer to two decimal places.

Accepted Answer

A)  $1.63 \mathrm {~m} ^ { 2 }$ 
B)  $2.66 \mathrm {~m} ^ { 2 }$ 
C)  $7.07 \mathrm {~m} ^ { 2 }$ 
D)  $0.03 \mathrm {~m} ^ { 2 }$ 
A)  $1.63 \mathrm {~m} ^ { 2 }$ 
B)  $2.66 \mathrm {~m} ^ { 2 }$ 
C)  $7.07 \mathrm {~m} ^ { 2 }$ 
D)  $0.03 \mathrm {~m} ^ { 2 }$

Factor out the greatest common factor. Simplify the factors, if possible. - $12 w x - 9 w y - 15 w z$

Factor by any method. - $b ^ { 6 } - 1$

Find the product. - $( p + 15 ) ^ { 2 }$

Find the product. - $- 5 a ^ { 3 } x ^ { 6 } \left( - 5 a ^ { 7 } x ^ { 8 } + 2 x ^ { 6 } + 4 a \right)$

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

Factor by any method. - $8 p ^ { 3 } - 1$

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

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 7,8,9,10,11,12,13,14,15,16,17 \} , \mathrm { M } = \{ 7,9,11,13 \} , \mathrm { N } = \{ 8,10,12,14,16 \}$ , $Q = \{ 7,9,11,13,15,17 \}$ , and $R = \{ 7,8,9,10 \}$ . $\mathrm { M } \cup \mathrm { N }$

Simplify the expression. Assume all variables represent positive real numbers. - $4 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }$

Divide. - $\frac { - 9 x ^ { 7 } - 9 x ^ { 6 } - 12 x ^ { 5 } } { - 3 x ^ { 6 } }$

Evaluate the expression. - $( - 6 ) ^ { 3 } - ( - 6 ) ^ { 2 }$

Find the sum or difference. - $\left( 5 x ^ { 4 } + 3 x ^ { 6 } - 5 + 7 x ^ { 5 } \right) - \left( 7 - 3 x ^ { 5 } + 8 x ^ { 6 } + 9 x ^ { 4 } \right)$

Use set notation, and list all the elements of the set. - $\{ 83,79,75 , \ldots , 43 \}$

Divide. - $\frac { 10 x ^ { 3 } + 5 x ^ { 2 } - 3 x - 1 } { - 2 x + 1 }$

Simplify the expression. Assume all variables represent positive real numbers. - $6 \sqrt [ 3 ] { 3 } + 11 \sqrt [ 3 ] { 3 }$

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - $- 11 x ^ { 3 } - 6 w ^ { 2 } - 6 w - 5 y ^ { 4 } - 2$

Identify the set as finite or infinite. - $\{ 8,16,24 , \ldots , 48 \}$

Find the product. - $( - 8 x - 9 ) ^ { 2 }$

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Exam 12: Review of Basic Concepts

Factor out the greatest common factor. Simplify the factors, if possible. - 12wx−9wy−15wz12 w x - 9 w y - 15 w z12wx−9wy−15wz

Factor by any method. - b6−1b ^ { 6 } - 1b6−1

Find the product. - (p+15)2( p + 15 ) ^ { 2 }(p+15)2

Find the product. - −5a3x6(−5a7x8+2x6+4a)- 5 a ^ { 3 } x ^ { 6 } \left( - 5 a ^ { 7 } x ^ { 8 } + 2 x ^ { 6 } + 4 a \right)−5a3x6(−5a7x8+2x6+4a)

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −19c5+4c4+4c3- 19 c ^ { 5 } + 4 c ^ { 4 } + 4 c ^ { 3 }−19c5+4c4+4c3

Factor by any method. - 8p3−18 p ^ { 3 } - 18p3−1

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - 1a+11a−1\frac { \frac { 1 } { a } + 1 } { \frac { 1 } { a } - 1 }a1​−1a1​+1​

Simplify the expression. Assume all variables represent positive real numbers. - 4a3+27a34 \sqrt [ 3 ] { a } + \sqrt [ 3 ] { 27 a }43a​+327a​

Divide. - −9x7−9x6−12x5−3x6\frac { - 9 x ^ { 7 } - 9 x ^ { 6 } - 12 x ^ { 5 } } { - 3 x ^ { 6 } }−3x6−9x7−9x6−12x5​

Evaluate the expression. - (−6)3−(−6)2( - 6 ) ^ { 3 } - ( - 6 ) ^ { 2 }(−6)3−(−6)2

Find the sum or difference. - (5x4+3x6−5+7x5)−(7−3x5+8x6+9x4)\left( 5 x ^ { 4 } + 3 x ^ { 6 } - 5 + 7 x ^ { 5 } \right) - \left( 7 - 3 x ^ { 5 } + 8 x ^ { 6 } + 9 x ^ { 4 } \right)(5x4+3x6−5+7x5)−(7−3x5+8x6+9x4)

Use set notation, and list all the elements of the set. - {83,79,75,…,43}\{ 83,79,75 , \ldots , 43 \}{83,79,75,…,43}

Divide. - 10x3+5x2−3x−1−2x+1\frac { 10 x ^ { 3 } + 5 x ^ { 2 } - 3 x - 1 } { - 2 x + 1 }−2x+110x3+5x2−3x−1​

Simplify the expression. Assume all variables represent positive real numbers. - 633+11336 \sqrt [ 3 ] { 3 } + 11 \sqrt [ 3 ] { 3 }633​+1133​

Identify the polynomial as a monomial, binomial, trinomial, or none of these. - −11x3−6w2−6w−5y4−2- 11 x ^ { 3 } - 6 w ^ { 2 } - 6 w - 5 y ^ { 4 } - 2−11x3−6w2−6w−5y4−2

Identify the set as finite or infinite. - {8,16,24,…,48}\{ 8,16,24 , \ldots , 48 \}{8,16,24,…,48}

Find the product. - (−8x−9)2( - 8 x - 9 ) ^ { 2 }(−8x−9)2