Deck 5: Polynomials and Factoring

Question 1

Rewrite the expression $\frac { 1 } { 2 z ^ { - 5 } }$ using only positive exponents. Assume that z is not zero.

A) $32 z ^ { 5 }$
B) $- \frac { z ^ { 5 } } { 2 }$
C) $\frac { z ^ { 5 } } { 2 }$
D) $2 z ^ { 5 }$
E) - $2 z ^ { 5 }$

Answer 1

$\frac { z ^ { 5 } } { 2 }$

Question 2

Simplify the expression $( s t ) ^ { 8 } \left( s ^ { 6 } t \right) ^ { 2 }$ .

A) $s ^ { 44 } t ^ { 32 }$
B) $s ^ { 37 } t ^ { 16 }$
C) $s ^ { 16 } t ^ { 10 }$
D) $s ^ { 96 } t ^ { 16 }$
E) $s ^ { 20 } t ^ { 10 }$

Answer 2

$s ^ { 20 } t ^ { 10 }$

Question 3

Rewrite the expression $3 x ^ { - 4 }$ using only positive exponents. Assume that x is not zero.

A) $\frac { 1 } { 81 x ^ { 4 } }$
B) $\frac { 3 } { x ^ { 4 } }$
C) $\frac { 1 } { 3 x ^ { 4 } }$
D) $- \frac { 3 } { x ^ { 4 } }$
E) $- \frac { 1 } { 81 x ^ { 4 } }$

Answer 3

$\frac { 3 } { x ^ { 4 } }$

Question 4

Simplify the expression $\frac { 5 ^ { 6 } u ^ { 9 } v ^ { 9 } } { 5 ^ { 8 } u ^ { 9 } v ^ { 3 } }$ . Assume that neither u nor v is zero.

A) $\frac { u v ^ { 6 } } { 10 }$
B) $\frac { v ^ { 6 } } { 25 }$
C) $\frac { v ^ { 6 } } { 10 }$
D) $\frac { v ^ { 3 } } { 25 }$
E) $\frac { u v ^ { 3 } } { 10 }$

Question 5

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n + 4 } y ^ { 5 n - 5 } } { x ^ { 3 n + 2 } y ^ { n - 2 } }$

A) $x ^ { n + 2 } y ^ { 4 n - 7 }$
B) $x ^ { n + 6 } y ^ { 4 n - 3 }$
C) $x ^ { 7 n + 2 } y ^ { 4 x - 3 }$
D) $x ^ { n + 2 } y ^ { 4 n - 3 }$
E) $x ^ { 7n+ 2 } y ^ { 4 n - 7 }$

Question 6

Use the rules of exponents to simplify the expression below. $\left[ \frac { \left( 2 x ^ { 2 } \right) ( 2 x ) ^ { 2 } } { \left( - 2 x ^ { 2 } \right) ( 2 x ) } \right] ^ { 2 }$

A) $4 x ^ { 2 }$
B) $- 6 x ^ { 5 }$
C) $3 x ^ { 2 }$
D) $14 x ^ { 7 }$
E) $5 x ^ { 6 }$

Question 7

Use the rules of exponents to simplify the expression $\left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { - 3 } \left( 2 x ^ { - 5 } y ^ { 5 } \right) ^ { 3 }$ using only positive exponents. Assume that no variable is zero.

A) $\frac { 64 y ^ { 30 } } { x ^ { 30 } }$
B)1
C) $\frac { 64 x ^ { 30 } } { y ^ { 30 } }$
D) $\frac { - 4 y ^ { 30 } } { x ^ { 30 } }$
E) 64

Question 8

Find the value of $\left( \frac { 6 } { 7 } \right) ^ { - 2 }$ .

A) $- \frac { 49 } { 36 }$
B) $\frac { 49 } { 36 }$
C) $\frac { 36 } { 49 }$
D) $\frac { 36 } { 7 }$
E) - $\frac { 36 } { 49 }$

Question 9

Use the rules of exponents to simplify the expression below.
$\left[ \frac { \left( 3 x ^ { 2 } \right) ( 3 x ) ^ { 2 } } { \left( - 3 x ^ { 2 } \right) ( 3 x ) } \right] ^ { 3 }$

A) $- 26 x ^ { 7 }$
B) $- 28 x ^ { 3 }$
C) $- 27 x ^ { 3 }$
D) $- 37 x ^ { 6 }$
E) $- 17 x ^ { 8 }$

Question 10

Rewrite the expression $\frac { 3 w ^ { 3 } } { 5 z ^ { - 3 } }$ using only positive exponents. Assume that z is not zero.

A) $\frac { 27 w ^ { 3 } z ^ { 3 } } { 5 }$
B) $375 w ^ { 3 } z ^ { 3 }$
C) $15 w ^ { 3 } z ^ { 3 }$
D) $\frac { 3 w ^ { 9 } z ^ { 9 } } { 5 }$
E) $\frac { 3 w ^ { 3 } z ^ { 3 } } { 5 }$

Question 11

Evaluate the expression $\left( \frac { 5 x } { 3 y } \right) ^ { - 1 }$ when x=-8 and y=9 .

A) $- \frac { 27 } { 40 }$
B) $\frac { 40 } { 27 }$
C) $\frac { 27 } { 40 }$
D) $- \frac { 40 } { 27 }$
E) $- \frac { 15 } { 8 }$

Question 12

Find the value of $( - 2 ) ^ { - 5 }$ .

A) $\frac { 1 } { 32 }$
B) -10
C) 10
D) $7,5$
E) - $\frac { 1 } { 32 }$

Question 13

Simplify the expression $\frac { 64 u ^ { 6 } } { 4 u ^ { 2 } }$ . Assume that u is not zero.

A) $16 u ^ { 3 }$
B) $8 u ^ { 4 }$
C) $16 u ^ { 4 }$
D) $8 u ^ { 3 }$
E) $8 u ^ { 8 }$

Question 14

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero. $\frac { s ^ { - 1 } + r ^ { - 1 } } { s ^ { - 1 } - r ^ { - 1 } }$

A) $\frac { r - s } { r + s }$
B) $s ^ { 2 } + r ^ { 2 }$
C) $\frac { r + s } { r - s }$
D) $\frac { s + r } { s - r }$
E) $\frac { s - r } { s + r }$

Question 15

Use the rules of exponents to simplify the expression below. $\frac { x ^ { 4 n } y ^ { 3 xn - 1 } } { x ^ { n } y ^ { n - 4 } }$

A) $x ^ { 3 } y ^ { 2 }$
B) $x ^ { 3 } y ^ { 2 n + 3 }$
C) $x ^ { 3 n } y ^ { 2 n + 3 }$
D) $x ^ { 2 } y ^ { 2 n + 3 }$
E) $x ^ { 2 n } y ^ { 2 n + 3 }$

Question 16

Evaluate the expression $\left( 9 + 3 ^ { - 4 } \right) ^ { 0 }$ .

A) $\frac { 730 } { 81 }$
B)0
C) 9
D)1
E) $\frac { 1 } { 81 }$

Question 17

Simplify the expression $\frac { 10 \left( u v ^ { 2 } \right) ^ { 3 } } { ( 5 u ) ^ { 3 } v ^ { 4 } }$ . Assume that neither u nor v is zero.

A) $\frac { 2 v ^ { 2 } } { 25 u ^ { 2 } }$
B) $\frac { 2 v ^ { 2 } } { 25 }$
C) $\frac { 2 v ^ { 4 } } { 5 u ^ { 2 } }$
D) $\frac { 2 v } { 5 }$
E) $\frac { 2 } { v ^ { 2 } }$

Question 18

Simplify the expression $\left( - 9 x ^ { 8 } \right) x ^ { 4 }$ .

A) $- 9 x ^ { 32 }$
B) $- 9 x ^ { 16 }$
C) $9 x ^ { - 12 }$
D) $- 9 x ^ { 12 }$
E) $9 x ^ { - 32 }$

Question 19

Rewrite the expression using only positive exponents, and simplify. Assume that any variables in the expression are nonzero.
$\frac { \left( 2 a ^ { - 3 } b ^ { 2 } \right) ^ { 3 } b } { \left( 10 a ^ { 4 } b \right) ^ { 4 } }$

A) $\frac { b ^ { 3 } } { 5 a ^ { 25 } }$
B) $\frac { b ^ { 3 } } { 1,250 a ^ { 25 } }$
C) $\frac { b ^ { 3 } } { 5 a ^ { 24 } }$
D) $\frac { b ^ { 2 } } { 5 a ^ { 24 } }$
E) $\frac { b ^ { 2 } } { 1,250 a ^ { 25 } }$

Question 20

Use the rules of exponents to simplify the expression $\left( 2 x ^ { 4 } y ^ { 6 } \right) ^ { - 2 }$ using only positive exponents. Assume that neither x nor y is 0.

A) $2 x ^ { 2 } y ^ { 4 }$
B) $\frac { 1 } { 4 x ^ { 8 } y ^ { 12 } }$
C) $\frac { 1 } { 2 x ^ { 8 } y ^ { 12 } }$
D) $4 x ^ { 2 } y ^ { 4 }$
E) $\frac { 2 } { x ^ { 8 } y ^ { 12 } }$

Question 21

The masses of Mercury and the sun are approximately $3.3 \times 10 ^ { 23 }$ kilograms and $1.99 \times 10 ^ { 30 }$ kilograms, respectively. The mass of the sun is approximately how many times that of Mercury?

A) 3,030 times
B) $6,030,303$ times
C) 16,470 times
D) 3,919 times
E) 84,200 times

Question 22

Write $9 \times 10 ^ { - 5 }$ in decimal notation.

A) $0.00009$
B) $900,000$
C) $9,000,000$
D) $0.000009$
E) $0.0009$

Question 23

Find the sum $\left( - 9 x ^ { 2 } - 8 x + 12 \right) + \left( - 2 x ^ { 3 } - 5 x ^ { 2 } - 12 \right)$ .

A) $- 2 x ^ { 3 } - 14 x ^ { 2 } - 8 x$
B) $- 11 x ^ { 5 } - 13 x ^ { 3 }$
C) $- 24 x ^ { 8 }$
D) $- 11 x ^ { 5 } - 13 x ^ { 3 } + 24$
E) $- 11 x ^ { 3 } - 13 x ^ { 2 } + 24$

Question 24

Find the difference $( - 9 x + 8 ) - ( 2 x + 4 )$ .

A) -11 x+2
B) -7x+12
C) $- 7 x ^ { 2 } + 12$
D) -11 x+4
E) $- 7 x ^ { 2 } + 4$

Question 25

Is the polynomial below a monomial, binomial, trinomial, or none of these? $4 x ^ { 3 }$

A)binomial
B)monomial
C)none of these
D)trinomial

Question 26

Find the sum of the polynomials. $\begin{array} { r } 6 x ^ { 2 } + 7 x - 2 \\7 x ^ { 2 } + 2 x - 2 \\- 6 x - 2 \\\hline\end{array}$

A) $13 x ^ { 4 } + 3 x ^ { 2 } - 6$
B) $13 x ^ { 2 } + 3 x - 2$
C) $16 x ^ { 7 } - 6$
D) $13 x ^ { 4 } + 3 x ^ { 2 } - 2$
E) $13 x ^ { 2 } + 3 x - 6$

Question 27

Find the sum of the polynomials. $\begin{array} { r } x ^ { 4 } + 9 x ^ { 3 } + 5 x + 7 \\8 x ^ { 3 } - 2 x - 7\\\hline\end{array}$

A) $x ^ { 4 } + 17 x ^ { 3 } + 3 x$
B) $17 x ^ { 3 } + 3 x$
C) $17 x ^ { 6 } + x ^ { 4 } + 3 x ^ { 2 }$
D) $x ^ { 4 } + 17 x ^ { 3 } + 3 x + 14$
E) $17 x ^ { 6 } + x ^ { 4 } + 3 x ^ { 2 } - 14$

Question 28

Find the difference $- 2 - \left( - 6 u ^ { 2 } - 8 \right)$ .

A) $6 u ^ { 2 } - 10$
B) $6 u ^ { 2 } + 6$
C) $4 u ^ { 2 } - 10$
D) $4 u ^ { 2 } + 6$
E) $- 6 u ^ { 2 } - 10$

Question 29

Write the number $5.92 \times 10 ^ { - 3 }$ in decimal notation.

A) $59,200$
B) 59.2
C) $0.00592$
D) $592,000$
E) 0.592

Question 30

Find the difference of the polynomials. $\begin{array} { l } x ^ { 4 } + 7 x ^ { 3 } + 5 x - 7 \\- \left( - 3 x ^ { 3 } + 2 x + 7 \right)\\\hline\end{array}$

A) $x ^ { 4 } + 10 x ^ { 3 } + 3 x - 14$
B) $x ^ { 4 } + 10 x ^ { 3 } + 7 x - 14$
C) $x ^ { 4 } + 10 x ^ { 3 } + 3 x + 14$
D) $x ^ { 4 } + 4 x ^ { 3 } + 3 x + 14$
E) $x ^ { 4 } + 4 x ^ { 3 } + 7 x + 14$

Question 31

Find the difference $\left( - 6 x ^ { 2 } + 4 x - 12 \right) - \left( 4 x ^ { 3 } + 2 x ^ { 2 } - 12 \right)$ .

A) $- 4 x ^ { 3 } - 8 x ^ { 2 } + 4 x$
B) $- 4 x ^ { 3 } - 4 x ^ { 2 } + 4 x$
C) $- 10 x ^ { 3 } + 2 x ^ { 2 } - 24$
D) $- 10 x ^ { 3 } + 2 x ^ { 2 }$
E) $- 4 x ^ { 3 } - 4 x ^ { 2 } - 24$

Question 32

Find the sum $\left( \frac { 5 } { 8 } x ^ { 3 } + 2 \right) + \left( \frac { 5 } { 16 } x ^ { 3 } - 5 \right)$ .

A) $\frac { 15 } { 16 } x ^ { 3 } - 3$
B) $\frac { 15 } { 16 } x ^ { 6 } - 3$
C) $15 x ^ { 3 } - 48$
D) $15 x ^ { 6 } - 48$
E) $\frac { 15 } { 16 } x ^ { 9 } - 3$

Question 33

Which of the following polynomials is a binomial of degree 3?

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

Question 34

Evaluate the expression $\frac { 2.6 \times 10 ^ { 5 } } { 1.3 \times 10 ^ { 3 } }$ . Write the answer in scientific notation.

A) $2 \times 10 ^ { 4 }$
B) $2 \times 10 ^ { 1 }$
C) $2 \times 10 ^ { 2 }$
D) $2 \times 10 ^ { 3 }$
E) $2 \times 10 ^ { - 2 }$

Question 35

Find the sum $( 6 x + 2 ) + ( 8 x - 6 )$ .

A) $48 x - 4$
B) 10x
C) 14x-4
D) $14 x ^ { 2 } - 4$
E) $10 x ^ { 2 }$

Question 36

Evaluate the expression below without a calculator. $\frac { 68000 } { 0.00001 }$

A) $6,800,000$
B) $68,000,000$
C) $68,000,000,000$
D) $6,800,000,000$
E) $680,000,000,000$

Question 37

Add $5 z - 4 z ^ { 2 } \text { to } 6 z ^ { 2 } + 6 z$ .

A) $11 z ^ { 4 } + 2 z ^ { 2 }$
B) $13 z ^ { 6 }$
C) $2 z ^ { 2 } + 11 z$
D) $11 z ^ { 2 } + 2 z$
E) $2 z ^ { 4 } + 11 z ^ { 2 }$

Question 38

Subtract $3 y ^ { 2 } - 3 y ^ { 3 } \text { from } 9 y ^ { 5 } + 9 y ^ { 3 }$ .

A) $6 y ^ { 3 } + 12$
B) $- 9 y ^ { 5 } - 12 y ^ { 3 } + 3 y ^ { 2 }$
C) $- 6 y ^ { 3 } - 12$
D) $9 y ^ { 5 } + 12 y ^ { 3 } - 3 y ^ { 2 }$
E) $6 y ^ { 5 } + 12 y ^ { 3 }$

Question 39

Write the polynomial $- 2 x - 6 x ^ { 4 } + 4 x ^ { 2 } + 7$ in standard form. Find the leading coefficient of the polynomial.

A) $7 + 4 x ^ { 2 } - 2 x - 6 x ^ { 4 }$ leading coefficient: 2
B) $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 7
C) $7 + 4 x ^ { 2 } - 2 x - 6 x ^ { 4 }$ leading coefficient: 7
D) $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 6
E) $- 6 x ^ { 4 } + 4 x ^ { 2 } - 2 x + 7$ leading coefficient: 2

Question 40

Write the number $0.00161$ in scientific notation.

A) $1.61 \times 10 ^ { - 4 }$
B) $1.61 \times 10 ^ { - 2 }$
C) $1.61 \times 10 ^ { - 3 }$
D) $1.61 \times 10 ^ { 3 }$
E) $1.61 \times 10 ^ { 2 }$

Question 41

An object is thrown upwards from the top of a building, which is 1296 feet tall. The initial velocity is 3 feet per second. Use the position function below to find the height of the object when t=2 seconds. $s = - 16 t ^ { 2 } + 3 t + 1296$

A)58 feet
B)1354 feet
C)1226 feet
D)1238 feet
E)1366 feet

Question 42

Perform the indicated operations and simplify. Assume that all exponents represent positive integers. $\left( - 2 x ^ { 3 n } + 2 x ^ { 2 n } - 4 x ^ { n } \right) - \left( 5 x ^ { 2 n } + 3 x ^ { n } - 2 \right)$

A) $- 2 x ^ { 3 n } - 3 x ^ { 2 n } - 7 x ^ { n } + 2$
B) $- 7 x ^ { 3 n } - 3 x ^ { 2 n } - 7 x ^ { n } + 2$
C) $- 7 x ^ { 3 n } - x ^ { 2 n } - 2 x ^ { n } - 2$
D) $- 2 x ^ { 3 n } + 7 x ^ { 2 n } - x ^ { n } - 2$
E) $- 7 x ^ { 3 n } - x ^ { 2 n } - 2 x ^ { n }$

Question 43

Perform the indicated operations and simplify. $2 \left( 4 t ^ { 2 } + 7 \right) - 8 \left( t ^ { 2 } + 7 \right) + 6 \left( 6 t ^ { 2 } + 7 \right)$

A) $36 t ^ { 2 } - 84$
B) $36 t ^ { 2 }$
C) $52 t ^ { 2 } + 28$
D) $- 36 t ^ { 2 } - 84$
E) $52 t ^ { 2 } + 112$

Question 44

Multiply: $9 y ( 8 y )$

A) $72 y ^ { 2 }$
B) $144 y$
C) 72y
D) 17y
E) $17 y ^ { 2 }$

Question 45

Find an expression for the area of the figure. Assume all angles are right angles. 6 x 9 x 4.5 x 3 x

A)
B)
C)
D)
E)

Question 46

Multiply: $- 9 x \left( 2 x ^ { 6 } - 5 x ^ { 3 } + 8 \right)$

A) $- 18 x ^ { 7 } + 45 x ^ { 4 } - 72 x$
B) $- 18 x ^ { 7 } + 5 x ^ { 3 } - 8 x$
C) $- 18 x ^ { 7 } - 45 x ^ { 4 } + 72 x$
D) $- 18 x ^ { 7 } + 45 x ^ { 4 } + 72 x$
E) $- 18 x ^ { 7 } - 5 x ^ { 3 } + 8 x$

Question 47

Find an expression for the perimeter of the figure. Assume all angles are right angles. 18z 6z

A)
B)
C)
D)
E)

Question 48

Perform the indicated operations and simplify. $- \left( - 5 x ^ { 2 } + 3 x + 17 \right) - \left( 3 x - 5 x ^ { 2 } + 17 \right)$ .

A) $10 x ^ { 2 } - 6 x - 34$
B)0
C)-34
D) $- 6 x - 34$
E) $10 x ^ { 2 } - 34$

Question 49

Find the height in feet of a free-falling object at time t=5 using the function $s = - 16 t ^ { 2 } + 76 t + 118$ .

A)138 feet
B)98 feet
C)20 feet
D)662 feet
E)898 feet

Question 50

Multiply: $\left( - 7 y ^ { 4 } \right) \left( - 3 y ^ { 3 } \right)$

A) $- 21 y ^ { 12 }$
B) $- 10 y ^ { 7 }$
C) $21 y ^ { 7 }$
D) $- 10 y ^ { 12 }$
E) $21 y ^ { 12 }$

Question 51

Find $h ( x ) = f ( x ) + g ( x )$ where $f ( x ) = 8 x ^ { 3 } - 9 x ^ { 2 } + 8$ and $g ( x ) = 10 - x - x ^ { 2 } - 9 x ^ { 3 }$

A) $h ( x ) = - x ^ { 3 } - 10 x ^ { 2 } - x + 18$
B) $h ( x ) = - x ^ { 6 } - 8 x ^ { 2 } - x - 2$
C) $h ( x ) = 17 x ^ { 3 } - 8 x ^ { 2 } - x - 2$
D) $h ( x ) = - 17 x ^ { 3 } - 8 x ^ { 2 } - x - 2$
E) $h ( x ) = - x ^ { 3 } - 10 x ^ { 2 } + x + 18$

Question 52

Find the height in feet of a free-falling object at time t=4 using the function $s = - 16 t ^ { 2 } + 63 t + 144$ .

A)652 feet
B)148 feet
C)4 feet
D)364 feet
E)140 feet

Question 53

Multiply: $- 9 u \left( - 5 u ^ { 2 } + 2 \right)$

A) $45 u ^ { 2 } - 18$
B) $45 u ^ { 3 } + 2$
C) $45 u ^ { 2 } + 2 u$
D) $45 u ^ { 3 } - 18$
E) $45 u ^ { 3 } - 18 u$

Question 54

Find the height in feet of a free-falling object at time t=2 using the function $s = - 16 t ^ { 2 } + 57 t + 53$ .

A)125 feet
B)231 feet
C)50 feet
D)3 feet
E)103 feet

Question 55

Perform the indicated operations and simplify. $\left( 8 x ^ { 2 } + 5 x + 6 \right) - \left[ \left( - 6 x ^ { 3 } + 3 x ^ { 2 } - 19 \right) + ( - 7 x + 11 ) \right]$

A) $- 6 x ^ { 3 } + 11 x ^ { 2 } + 12 x + 14$
B) $6 x ^ { 3 } + 5 x ^ { 2 } - 2 x - 2$
C) $6 x ^ { 3 } + 11 x ^ { 2 } - 2 x - 2$
D) $6 x ^ { 3 } + 5 x ^ { 2 } + 12 x + 14$
E) $- 6 x ^ { 3 } + 5 x ^ { 2 } - 2 x - 2$

Question 56

Multiply the two polynomials using the FOIL Method. $\left( x + \frac { 1 } { 5 } \right) ( 15 x - 10 )$

A) $15 x ^ { 2 } - 7 x - 2$
B) $15 x ^ { 2 } - 7 x + 2$
C) $15 x ^ { 2 } + 7 x + 2$
D) $15 x ^ { 2 } + 13 x + 2$
E) $15 x ^ { 2 } - 13 x - 2$

Question 57

Multiply $( 8 x - 8 ) ( 3 x - 4 )$ and simplify.

A) $24 x ^ { 2 } - 56 x + 32$
B) $24 x + 32$
C) $24 x ^ { 2 } - 16 x + 32$
D) $24 x ^ { 2 } + 11 x + 32$
E) $24 x ^ { 2 } + 32$

Question 58

Find the difference $\left( 9 x ^ { 2 } + 4 x - 10 \right) - \left( 4 x + 9 x ^ { 2 } - 10 \right)$ .

A)-20
B)0
C) $8 x - 20$
D) $18 x - 20$
E) $8 x ^ { 2 } + 8 x - 20$

Question 59

Find the height in feet of a free-falling object at time t=0 using the function $s = - 16 t ^ { 2 } + 11 t + 30$ .

A)30 feet
B)32 feet
C)22 feet
D)60 feet
E)16 feet

Question 60

Perform the indicated operations and simplify. $\left( 7 x ^ { 4 } + 3 x ^ { 2 } \right) + 3 \left( - 5 x ^ { 4 } - 5 x ^ { 2 } \right)$

A) $- 8 x ^ { 4 } - 12 x ^ { 2 }$
B) $22 x ^ { 4 } + 18 x ^ { 2 }$
C) $22 x ^ { 4 } - 2 x ^ { 2 }$
D) $22 x ^ { 4 } - 12 x ^ { 2 }$
E) $- 8 x ^ { 4 } - 2 x ^ { 2 }$

Question 61

Use a special product pattern to find the product $( x + 9 ) ( x - 9 )$ .

A) $x ^ { 2 } - 18 x + 81$
B) $x ^ { 2 } - 81$
C) $x ^ { 2 } + 81$
D) $x ^ { 2 } + 18 x + 81$
E) $x ^ { 2 } - 18$

Question 62

Use a special product pattern to find the product $\left( 9 x ^ { 2 } + 8 \right) \left( 9 x ^ { 2 } - 8 \right)$ .

A) $81 x ^ { 2 } - 64$
B) $81 x ^ { 2 } - 72 x + 64$
C) $81 x ^ { 4 } - 144 x ^ { 2 } + 64$
D) $81 x ^ { 4 } - 17 x ^ { 2 } - 64$
E) $81 x ^ { 4 } - 64$

Question 63

Use a vertical format to find the product of the two polynomials. $\left( 3 x ^ { 2 } - 4 x - 4 \right) \left( 3 x ^ { 2 } - 4 x - 1 \right)$

A) $9 x ^ { 5 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x + 4$
B) $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x + 4$
C) $9 x ^ { 4 } - 24 x ^ { 3 } + 20 x + 4$
D) $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 4$
E) $9 x ^ { 4 } - 24 x ^ { 3 } + x ^ { 2 } + 20 x$

Question 64

Use a special product pattern to find the product $( 7 x + 1 ) ^ { 2 }$ .

A) $49 x ^ { 2 } - 1$
B) $49 x ^ { 2 } + 16 x + 1$
C) $49 x ^ { 2 } + 1$
D) $49 x ^ { 2 } + 7 x + 1$
E) $49 x ^ { 2 } + 14 x + 1$

Question 65

A closed rectangular box has dimensions of length n inches, width n+6 inches, and height n+2 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box.

A) $A ( n ) = n ^ { 2 } - 2 n + 12$
B) $A ( n ) = - n ^ { 2 } + 6 n + 12$
C) $A ( n ) = n ^ { 2 } - 4 n + 12$
D) $A ( n ) = n ^ { 2 } + 4 n + 12$
E) $A ( n ) = n ^ { 2 } + 8 n + 12$

Question 66

Simplify the expression. Assume that all variables represent positive integers. $\left( x ^ { y + 5 } \right) ^ { y - 5 }$

A) $x ^ { y^ { 2 } - s ^ { 2 } }$
B) $x ^ { y ^ { 2 } + 2 y 5 + 5 ^ { 2 } }$
C) $x ^ { y ^ { 2 } + s ^ { 2 } }$
D) $x ^ { y ^ { 2 } - 2y5 - 5 ^ { 2 } }$
E) $x ^ { y ^ { 2 } + 2y5 - 5 ^ { 2 } }$

Question 67

A closed rectangular box has dimensions of length n inches, width inches, and height inches. What is the volume if the shortest side is 7 inches long?

A)189 cubic inches
B)495 cubic inches
C)320 cubic inches
D)96 cubic inches
E)1001 cubic inches

Question 68

Multiply the polynomials and simplify. $\begin{array} { r } x ^ { 2 } + 5 x - 6 \\\times \quad 3 x + 4 \\\hline\end{array}$

A) $3 x ^ { 3 } + 19 x ^ { 2 } + 5 x - 6$
B) $3 x ^ { 3 } + 4 x ^ { 2 } + 2 x - 24$
C) $3 x ^ { 3 } + 19 x ^ { 2 } + 2 x - 24$
D) $3 x ^ { 3 } + 4 x ^ { 2 } + 20 x - 6$
E) $3 x ^ { 3 } + 20 x ^ { 2 } - 6$

Question 69

Write a simplified expression for the area of the shaded region of the figure below.

A) $\text { 3. } 5 x ^ { 2 } + 14 x$
B) $4.5 x ^ { 2 } + 14.5 x$
C) $3.5 x ^ { 2 } + 10.5 x$
D) $4.5 x ^ { 2 } + 9 x$
E) $3.5 x ^ { 2 } + 7 x$

Question 70

Expand $( x - 3 ) ^ { 3 }$ and simplify.

A) $x ^ { 3 } - 27$
B) $x ^ { 3 } - 9 x ^ { 2 } + 27 x - 27$
C) $x ^ { 3 } + 27 x ^ { 2 } - 9 x - 27$
D) $x ^ { 3 } - 27 x ^ { 2 } + 9 x - 27$
E) $x ^ { 3 } - 3 x ^ { 2 } + 9 x - 27$

Question 71

Use a special product formula to find the product. $( 0.1 x + 0.4 ) ( 0.1 x - 0.4 )$

A) $0.01 x ^ { 2 } - 0.16$
B) $0.01 x ^ { 2 } - 0.08 x + 0.16$
C) $0.01 x ^ { 2 } + 0.16$
D) $0.01 x ^ { 2 } + 0.08 x - 0.16$
E) $0.01 x ^ { 2 } - 0.04 x + 0.16$

Question 72

Use a special product pattern to find the product $( x - 8 ) ^ { 2 }$ .

A) $x ^ { 2 } - 16 x + 64$
B) $x ^ { 2 } - 64$
C) $x ^ { 2 } + 64$
D) $x ^ { 2 } + 16 x + 64$
E) $x ^ { 2 } - 8 x + 64$

Question 73

A closed rectangular box has dimensions of length n inches, width n-4 inches, and height n+2 inches. Write a polynomial function $V ( n )$ that represents the volume of the box.

A) $V ( n ) = n ^ { 3 } + 2 n ^ { 2 } - 8$
B) $V ( n ) = n ^ { 3 } + 2 n ^ { 2 } - 8 n$
C) $V ( n ) = n ^ { 3 } - 2 n ^ { 2 } - 8 n$
D) $V ( n ) = n ^ { 3 } - 4 n ^ { 2 } - 8 n$
E) $V ( n ) = n ^ { 3 } + 6 n ^ { 2 } - 8 n$

Question 74

Use a special product pattern to find the product $[ 9 u + ( v + 10 ) ] ^ { 2 }$ .

A) $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 180 u + 20 v + 100$
B) $81 u ^ { 2 } + v ^ { 2 } + 20 v + 100$
C) $81 u ^ { 2 } + v ^ { 2 } + 180 u + 20 v + 100$
D) $81 u ^ { 2 } + v ^ { 2 } + 100$
E) $81 u ^ { 2 } + v ^ { 2 } + 18 u v + 20 v + 100$

Question 75

A closed rectangular box has dimensions of length n inches, width n+4 inches, and height n+5 inches. Write a polynomial function $A ( n )$ for the area of the largest side of the box if dimensions increase by 6 inches.

A) $A ( n ) = n ^ { 2 } + 4 n - 116$
B) $A ( n ) = n ^ { 2 } - 11 n + 110$
C) $A ( n ) = n ^ { 2 } + 4 n + 110$
D) $A ( n ) = n ^ { 2 } + 21 n + 110$
E) $A ( n ) = n ^ { 2 } + 11 n + 110$

Question 76

Multiply $( 3 x + 5 ) \left( x ^ { 2 } + 9 x - 2 \right)$ and simplify.

A) $3 x ^ { 3 } + 32 x ^ { 2 } + 9 x - 2$
B) $3 x ^ { 3 } + 5 x ^ { 2 } + 45 x - 2$
C) $3 x ^ { 3 } + 45 x ^ { 2 } - 2$
D) $3 x ^ { 3 } + 5 x ^ { 2 } + 39 x - 10$
E) $3 x ^ { 3 } + 32 x ^ { 2 } + 39 x - 10$

Question 77

Use a special product pattern to find the product. $( u - ( v - 2 ) ) ( u + ( v - 2 ) )$

A) $u ^ { 2 } + ( v - 2 ) ^ { 2 }$
B) $u ^ { 2 } - ( v - 2 ) ^ { 2 }$
C) $u ^ { 2 } - 2 u ( v - 2 ) + ( v - 2 ) ^ { 2 }$
D) $u ^ { 2 } - 2 u ( v - 2 ) - ( v - 2 ) ^ { 2 }$
E) $u ^ { 2 } + 2 u ( v - 2 ) - ( v - 2 ) ^ { 2 }$

Question 78

Multiply $\left( x ^ { 2 } + 4 x - 4 \right) \left( 5 x ^ { 2 } + 2 \right)$ and simplify.

A) $5 x ^ { 4 } + 8 x - 8$
B) $5 x ^ { 4 } + 24 x ^ { 3 } + 8 x - 8$
C) $5 x ^ { 4 } + 20 x ^ { 3 } - 18 x ^ { 2 } + 8 x - 8$
D) $5 x ^ { 4 } + 20 x ^ { 3 } + 2 x ^ { 2 } - 8$
E) $5 x ^ { 4 } + 24 x ^ { 3 } - 20 x ^ { 2 } + 8 x - 8$

Question 79

After 2 years, an investment of $1500 compounded annually at interest rate r will yield $1500 ( 1 + r ) ^ { 2 }$ . Find this product.

A) $r ^ { 2 } + 2 r + 1500$
B) $1500 r ^ { 2 } + 3000 r + 1500$
C) $1500 r ^ { 2 } + 1500 r + 1500$
D) $1500 r ^ { 2 } + 1500$
E) $3000 r ^ { 2 } + 1500 r + 1500$

Question 80

Use a special product pattern to find the product $( 7 x + 2 ) ( 7 x - 2 )$ .

A) $49 x ^ { 2 } - 4$
B) $49 x ^ { 2 } - 28 x + 4$
C) $49 x ^ { 2 } + 4$
D) $49 x ^ { 2 } - 9 x - 4$
E) $49 x ^ { 2 } - 14 x + 4$