Question 1

Use the quotient rule to simplify the expression.
-$\frac { y ^ { 16 } } { y ^ { 15 } }$

Accepted Answer

A)  $y$ 
B)  $\frac { 1 } { \mathrm {~V} }$ 
C)  $y ^ { 31 }$ 
D)  $\mathrm { y } ^ { 16 } - \mathrm { y } ^ { 15 }$ 
A)  $y$ 
B)  $\frac { 1 } { \mathrm {~V} }$ 
C)  $y ^ { 31 }$ 
D)  $\mathrm { y } ^ { 16 } - \mathrm { y } ^ { 15 }$

Question 2

Fill in the blank with one of the words or phrases listed below.

-The is the sum of the exponents on the variables in the term.

Accepted Answer

A)  degree of a polynomial 
B)  degree of a term 
C)  term 
D)  coefficient 
A)  degree of a polynomial 
B)  degree of a term 
C)  term 
D)  coefficient

Question 3

Find the perimeter.
-

Accepted Answer

A)  $\left( x ^ { 2 } + 4 x + 26 \right)$ units 
B)  $\left( 2 x ^ { 2 } + 8 x + 26 \right)$ units 
C)  $\left( 2 x ^ { 2 } + 8 x + 52 \right)$ units 
D)  $\left( 2 x ^ { 2 } + 12 x + 52 \right)$ units 
A)  $\left( x ^ { 2 } + 4 x + 26 \right)$ units 
B)  $\left( 2 x ^ { 2 } + 8 x + 26 \right)$ units 
C)  $\left( 2 x ^ { 2 } + 8 x + 52 \right)$ units 
D)  $\left( 2 x ^ { 2 } + 12 x + 52 \right)$ units

Question 4

Perform the division.
-$\frac { - 18 x ^ { 7 } + 15 x ^ { 5 } - 12 x ^ { 3 } } { - 3 x ^ { 5 } }$

Accepted Answer

A)  $6 x ^ { 2 } - 5 + \frac { 4 } { x }$ 
B)  $6 x - 5 + \frac { 4 } { x ^ { 2 } }$ 
C)  $6 x ^ { 2 } - 5 + \frac { 4 } { x ^ { 2 } }$ 
D)  $6 x - 5 + \frac { 4 } { x }$ 
A)  $6 x ^ { 2 } - 5 + \frac { 4 } { x }$ 
B)  $6 x - 5 + \frac { 4 } { x ^ { 2 } }$ 
C)  $6 x ^ { 2 } - 5 + \frac { 4 } { x ^ { 2 } }$ 
D)  $6 x - 5 + \frac { 4 } { x }$

Question 5

Solve.
-A wooden beam is $\left( 4 y ^ { 2 } + 4 y + 1 \right)$ feet long. If a piece $\left( y ^ { 2 } - 12 \right)$ feet is cut, express the length of the remaining piece of beam as a polynomial in $\mathrm { y }$.

Accepted Answer

A)  $3 y ^ { 2 } + 16 y + 1 f t$ 
B)  $3 y ^ { 2 } + 4 y - 11 f t$ 
C)  $3 y ^ { 2 } - 8 y + 1 f t$ 
D)  $3 y ^ { 2 } + 4 y + 13 f t$ 
A)  $3 y ^ { 2 } + 16 y + 1 f t$ 
B)  $3 y ^ { 2 } + 4 y - 11 f t$ 
C)  $3 y ^ { 2 } - 8 y + 1 f t$ 
D)  $3 y ^ { 2 } + 4 y + 13 f t$

Question 6

Write the number in standard notation.
-$4.898 \times 10 ^ { - 5 }$

Accepted Answer

A)  $0.0004898$ 
B)  $- 489,800$ 
C)  $0.000004898$ 
D)  $0.00004898$ 
A)  $0.0004898$ 
B)  $- 489,800$ 
C)  $0.000004898$ 
D)  $0.00004898$

Question 7

Multiply.
-$( 7 x + 12 ) ^ { 2 }$

Accepted Answer

A)  $7 x ^ { 2 } + 168 x + 144$ 
B)  $49 x ^ { 2 } + 168 x + 144$ 
C)  $49 x ^ { 2 } + 144$ 
D)  $7 x ^ { 2 } + 144$ 
A)  $7 x ^ { 2 } + 168 x + 144$ 
B)  $49 x ^ { 2 } + 168 x + 144$ 
C)  $49 x ^ { 2 } + 144$ 
D)  $7 x ^ { 2 } + 144$

Question 8

Use the quotient rule to simplify the expression.
-$\frac { 63 m ^ { 20 } n ^ { 11 } } { 7 m ^ { 19 } n ^ { 6 } }$

Accepted Answer

A)  $63 \mathrm { mn } ^ { 5 }$ 
B)  $9 m ^ { 39 } n ^ { 17 }$ 
C)  $9 n ^ { 5 }$ 
D)  $9 \mathrm { mn } ^ { 5 }$ 
A)  $63 \mathrm { mn } ^ { 5 }$ 
B)  $9 m ^ { 39 } n ^ { 17 }$ 
C)  $9 n ^ { 5 }$ 
D)  $9 \mathrm { mn } ^ { 5 }$

Question 9

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$P ( x ) = - 4 x ^ { 2 } - 4 x - 7 ; - 3$

Accepted Answer

A)  $- 55$ 
B)  17 
C)  $- 31$ 
D)  41 
A)  $- 55$ 
B)  17 
C)  $- 31$ 
D)  41

Question 10

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of
these.
-$11 a ^ { 10 }$

Accepted Answer

A)  11; binomial 
B)  10; binomial 
C)  11; monomial 
D)  10; monomial 
A)  11; binomial 
B)  10; binomial 
C)  11; monomial 
D)  10; monomial

Question 11

Perform the indicated operation.
-$$\begin{array} { r } 
5 x ^ { 9 } + 3 x ^ { 8 } + 4 x ^ { 7 } - 1 \
- \left( 7 x ^ { 9 } + 7 x ^ { 8 } - 6 x ^ { 7 } - 7 \right) \
\hline
\end{array}$$

Accepted Answer

A)  $12 x ^ { 9 } + 10 x ^ { 8 } - 2 x ^ { 7 } + 6$ 
B)  $- 2 x ^ { 9 } - 4 x ^ { 8 } + 10 x ^ { 7 } + 6$ 
C)  $12 x ^ { 9 } + 10 x ^ { 8 } - 2 x ^ { 7 } - 8$ 
D)  $- 2 x ^ { 9 } + 10 x ^ { 8 } - 2 x ^ { 7 } - 8$ 
A)  $12 x ^ { 9 } + 10 x ^ { 8 } - 2 x ^ { 7 } + 6$ 
B)  $- 2 x ^ { 9 } - 4 x ^ { 8 } + 10 x ^ { 7 } + 6$ 
C)  $12 x ^ { 9 } + 10 x ^ { 8 } - 2 x ^ { 7 } - 8$ 
D)  $- 2 x ^ { 9 } + 10 x ^ { 8 } - 2 x ^ { 7 } - 8$

Question 12

Perform the indicated operation.
-$$\begin{array} { r } 
2 n ^ { 5 } + 8 n ^ { 2 } - 12 \
- \left( 5 n ^ { 5 } - 2 n ^ { 2 } + 4 \right) \
\hline
\end{array}$$

Accepted Answer

A)  $- 3 n ^ { 5 } + 13 n ^ { 2 } - 8$ 
B)  $- 3 n ^ { 5 } + 10 n ^ { 2 } - 16$ 
C)  $- 9 n ^ { 7 }$ 
D)  $- 3 n ^ { 5 } + 10 n ^ { 2 } - 8$ 
A)  $- 3 n ^ { 5 } + 13 n ^ { 2 } - 8$ 
B)  $- 3 n ^ { 5 } + 10 n ^ { 2 } - 16$ 
C)  $- 9 n ^ { 7 }$ 
D)  $- 3 n ^ { 5 } + 10 n ^ { 2 } - 8$

Question 13

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c).
-$P ( x ) = x ^ { 2 } + 15 x + 47 ; - 8$

Accepted Answer

A)  7 
B)  $- 9$ 
C)  9 
D)  0 
A)  7 
B)  $- 9$ 
C)  9 
D)  0

Question 14

Solve.
-The square has sides of length $5 x ^ { 4 }$ centimeters. Find its area. $\left( A = s ^ { 2 } \right)$

Accepted Answer

A)  $25 \mathrm { x } ^ { 16 } \mathrm { sq } \mathrm { cm }$ 
B)  $10 x ^ { 8 } \mathrm { sq } \mathrm { cm }$ 
C)  $10 x ^ { 16 } \mathrm { sq } \mathrm { cm }$ 
D)  $25 \mathrm { x } ^ { 8 } \mathrm { sq } \mathrm { cm }$ 
A)  $25 \mathrm { x } ^ { 16 } \mathrm { sq } \mathrm { cm }$ 
B)  $10 x ^ { 8 } \mathrm { sq } \mathrm { cm }$ 
C)  $10 x ^ { 16 } \mathrm { sq } \mathrm { cm }$ 
D)  $25 \mathrm { x } ^ { 8 } \mathrm { sq } \mathrm { cm }$

Question 15

Multiply.
-$5 x ^ { 2 } \left( 6 x ^ { 2 } + 3 x - 7 \right)$

Accepted Answer

A)  $30 x ^ { 4 } + 15 x - 35$ 
B)  $11 x ^ { 4 } + 8 x - 2$ 
C)  $30 x ^ { 4 } + 15 x ^ { 3 } - 35 x ^ { 2 }$ 
D)  $30 x ^ { 4 } + 15 x ^ { 2 } - 35$ 
A)  $30 x ^ { 4 } + 15 x - 35$ 
B)  $11 x ^ { 4 } + 8 x - 2$ 
C)  $30 x ^ { 4 } + 15 x ^ { 3 } - 35 x ^ { 2 }$ 
D)  $30 x ^ { 4 } + 15 x ^ { 2 } - 35$

Question 16

Solve.
-Find the volume of the rectangular solid. Express the volume as a product, then multiply and simplify.

Accepted Answer

A)  $4 x ^ { 3 } - 38 x ^ { 2 } + 84 x$ 
B)  $4 x ^ { 2 } - 38 x + 85$ 
C)  $- 4 x ^ { 2 } + 18 x + 85$ 
D)  $- 4 x ^ { 3 } + 18 x ^ { 2 } + 84 x$ 
A)  $4 x ^ { 3 } - 38 x ^ { 2 } + 84 x$ 
B)  $4 x ^ { 2 } - 38 x + 85$ 
C)  $- 4 x ^ { 2 } + 18 x + 85$ 
D)  $- 4 x ^ { 3 } + 18 x ^ { 2 } + 84 x$

Question 17

Perform the indicated operation.
-$\left( 2 x ^ { 5 } - 2 x ^ { 4 } + 9 x ^ { 3 } + 3 \right) + \left( 9 x ^ { 5 } - 8 x ^ { 4 } + 9 x ^ { 3 } + 1 \right)$

Accepted Answer

A)  $11 x ^ { 5 } - 10 x ^ { 4 } + 18 x ^ { 3 } + 4$ 
B)  $- 5 x ^ { 5 } - 5 x ^ { 4 } + 3 x ^ { 3 } + 7$ 
C)  19 x24 + 4 
D)  $11 x ^ { 10 } - 10 x ^ { 8 } + 18 x ^ { 6 } + 4$ 
A)  $11 x ^ { 5 } - 10 x ^ { 4 } + 18 x ^ { 3 } + 4$ 
B)  $- 5 x ^ { 5 } - 5 x ^ { 4 } + 3 x ^ { 3 } + 7$ 
C)  19 x24 + 4 
D)  $11 x ^ { 10 } - 10 x ^ { 8 } + 18 x ^ { 6 } + 4$

Question 18

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of
these.
-$16 z - 2$

Accepted Answer

A)  0; binomial 
B)  1; binomial 
C)  16; monomial 
D)  2; binomial 
A)  0; binomial 
B)  1; binomial 
C)  16; monomial 
D)  2; binomial

Question 19

Perform the indicated operation.
-$\left( 18 y ^ { 2 } + 15 \right) - \left( - 7 y ^ { 4 } - 9 y ^ { 2 } + 15 \right)$

Accepted Answer

A)  $34 \mathrm { y } ^ { 6 }$ 
B)  $7 y ^ { 4 } + 27 y ^ { 2 }$ 
C)  $7 y ^ { 4 } + 27 y ^ { 2 } - 30$ 
D)  $- 7 y ^ { 4 } + 9 y ^ { 2 } + 30$ 
A)  $34 \mathrm { y } ^ { 6 }$ 
B)  $7 y ^ { 4 } + 27 y ^ { 2 }$ 
C)  $7 y ^ { 4 } + 27 y ^ { 2 } - 30$ 
D)  $- 7 y ^ { 4 } + 9 y ^ { 2 } + 30$

Question 20

Find the perimeter.
-

Accepted Answer

A)  $\left( 2 x ^ { 2 } + 9 x + 40 \right)$ units 
B)  $\left( 2 x ^ { 2 } + 9 x + 43 \right)$ units 
C)  $\left( x ^ { 2 } + 7 x + 43 \right)$ units 
D)  $\left( 2 x ^ { 2 } + 7 x + 43 \right)$ units 
A)  $\left( 2 x ^ { 2 } + 9 x + 40 \right)$ units 
B)  $\left( 2 x ^ { 2 } + 9 x + 43 \right)$ units 
C)  $\left( x ^ { 2 } + 7 x + 43 \right)$ units 
D)  $\left( 2 x ^ { 2 } + 7 x + 43 \right)$ units

Use the quotient rule to simplify the expression. - $\frac { y ^ { 16 } } { y ^ { 15 } }$

Fill in the blank with one of the words or phrases listed below. -The is the sum of the exponents on the variables in the term.

Find the perimeter. -

Perform the division. - $\frac { - 18 x ^ { 7 } + 15 x ^ { 5 } - 12 x ^ { 3 } } { - 3 x ^ { 5 } }$

Write the number in standard notation. - $4.898 \times 10 ^ { - 5 }$

Multiply. - $( 7 x + 12 ) ^ { 2 }$

Use the quotient rule to simplify the expression. - $\frac { 63 m ^ { 20 } n ^ { 11 } } { 7 m ^ { 19 } n ^ { 6 } }$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = - 4 x ^ { 2 } - 4 x - 7 ; - 3$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $11 a ^ { 10 }$

Perform the indicated operation. - 5+3+4-1 - 7+7-6-7

Perform the indicated operation. - 2+8-12 - 5-2+4

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 2 } + 15 x + 47 ; - 8$

Solve. -The square has sides of length $5 x ^ { 4 }$ centimeters. Find its area. $\left( A = s ^ { 2 } \right)$ $Solve. -The square has sides of length 5 x ^ { 4 } centimeters. Find its area. \left( A = s ^ { 2 } \right)$

Multiply. - $5 x ^ { 2 } \left( 6 x ^ { 2 } + 3 x - 7 \right)$

Solve. -Find the volume of the rectangular solid. Express the volume as a product, then multiply and simplify.

Perform the indicated operation. - $\left( 2 x ^ { 5 } - 2 x ^ { 4 } + 9 x ^ { 3 } + 3 \right) + \left( 9 x ^ { 5 } - 8 x ^ { 4 } + 9 x ^ { 3 } + 1 \right)$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $16 z - 2$

Perform the indicated operation. - $\left( 18 y ^ { 2 } + 15 \right) - \left( - 7 y ^ { 4 } - 9 y ^ { 2 } + 15 \right)$

Find the perimeter. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 5: Exponents and Polynomials

Use the quotient rule to simplify the expression. - y16y15\frac { y ^ { 16 } } { y ^ { 15 } }y15y16​

Fill in the blank with one of the words or phrases listed below. -The is the sum of the exponents on the variables in the term.

Find the perimeter. -

Perform the division. - −18x7+15x5−12x3−3x5\frac { - 18 x ^ { 7 } + 15 x ^ { 5 } - 12 x ^ { 3 } } { - 3 x ^ { 5 } }−3x5−18x7+15x5−12x3​

Solve. -A wooden beam is (4y2+4y+1)\left( 4 y ^ { 2 } + 4 y + 1 \right)(4y2+4y+1) feet long. If a piece (y2−12)\left( y ^ { 2 } - 12 \right)(y2−12) feet is cut, express the length of the remaining piece of beam as a polynomial in y\mathrm { y }y .

Write the number in standard notation. - 4.898×10−54.898 \times 10 ^ { - 5 }4.898×10−5

Multiply. - (7x+12)2( 7 x + 12 ) ^ { 2 }(7x+12)2

Use the quotient rule to simplify the expression. - 63m20n117m19n6\frac { 63 m ^ { 20 } n ^ { 11 } } { 7 m ^ { 19 } n ^ { 6 } }7m19n663m20n11​

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=−4x2−4x−7;−3P ( x ) = - 4 x ^ { 2 } - 4 x - 7 ; - 3P(x)=−4x2−4x−7;−3

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - 11a1011 a ^ { 10 }11a10

Perform the indicated operation. - 5+3+4-1 - 7+7-6-7

Perform the indicated operation. - 2+8-12 - 5-2+4

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - P(x)=x2+15x+47;−8P ( x ) = x ^ { 2 } + 15 x + 47 ; - 8P(x)=x2+15x+47;−8

Solve. -The square has sides of length 5x45 x ^ { 4 }5x4 centimeters. Find its area. (A=s2)\left( A = s ^ { 2 } \right)(A=s2)

Multiply. - 5x2(6x2+3x−7)5 x ^ { 2 } \left( 6 x ^ { 2 } + 3 x - 7 \right)5x2(6x2+3x−7)

Solve. -Find the volume of the rectangular solid. Express the volume as a product, then multiply and simplify.

Perform the indicated operation. - (2x5−2x4+9x3+3)+(9x5−8x4+9x3+1)\left( 2 x ^ { 5 } - 2 x ^ { 4 } + 9 x ^ { 3 } + 3 \right) + \left( 9 x ^ { 5 } - 8 x ^ { 4 } + 9 x ^ { 3 } + 1 \right)(2x5−2x4+9x3+3)+(9x5−8x4+9x3+1)

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - 16z−216 z - 216z−2

Perform the indicated operation. - (18y2+15)−(−7y4−9y2+15)\left( 18 y ^ { 2 } + 15 \right) - \left( - 7 y ^ { 4 } - 9 y ^ { 2 } + 15 \right)(18y2+15)−(−7y4−9y2+15)

Find the perimeter. -

Review of Real Numbers

Equations, Inequalities, and Problem Solving

Graphing

Solving Systems of Linear Equations

Factoring Polynomials

Rational Expressions

More on Functions and Graphs

Inequalities and Absolute Value

Rational Exponents, Radicals, and Complex Numbers

Quadratic Equations and Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Use the quotient rule to simplify the expression. - $\frac { y ^ { 16 } } { y ^ { 15 } }$

Perform the division. - $\frac { - 18 x ^ { 7 } + 15 x ^ { 5 } - 12 x ^ { 3 } } { - 3 x ^ { 5 } }$

Write the number in standard notation. - $4.898 \times 10 ^ { - 5 }$

Multiply. - $( 7 x + 12 ) ^ { 2 }$

Use the quotient rule to simplify the expression. - $\frac { 63 m ^ { 20 } n ^ { 11 } } { 7 m ^ { 19 } n ^ { 6 } }$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = - 4 x ^ { 2 } - 4 x - 7 ; - 3$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $11 a ^ { 10 }$

For the given polynomial P(x) and the given c, use the remainder theorem to find P(c). - $P ( x ) = x ^ { 2 } + 15 x + 47 ; - 8$

Solve. -The square has sides of length $5 x ^ { 4 }$ centimeters. Find its area. $\left( A = s ^ { 2 } \right)$ $Solve. -The square has sides of length 5 x ^ { 4 } centimeters. Find its area. \left( A = s ^ { 2 } \right)$

Multiply. - $5 x ^ { 2 } \left( 6 x ^ { 2 } + 3 x - 7 \right)$

Perform the indicated operation. - $\left( 2 x ^ { 5 } - 2 x ^ { 4 } + 9 x ^ { 3 } + 3 \right) + \left( 9 x ^ { 5 } - 8 x ^ { 4 } + 9 x ^ { 3 } + 1 \right)$

Find the degree of the following polynomial and determine whether it is a monomial, binomial, trinomial, or none of these. - $16 z - 2$

Perform the indicated operation. - $\left( 18 y ^ { 2 } + 15 \right) - \left( - 7 y ^ { 4 } - 9 y ^ { 2 } + 15 \right)$