Question 1

Subtract the polynomials.
-$\left( 8 x ^ { 6 } - 8 x ^ { 4 } + 12 \right) - \left( 4 x ^ { 6 } + 13 x ^ { 4 } - 8 \right)$

Accepted Answer

A)  $4 x ^ { 6 } - 21 x ^ { 4 } + 20$ 
B)  $4 x ^ { 6 } - 4 x ^ { 4 } + 4$ 
C)  $3 x ^ { 10 }$ 
D)  $4 x ^ { 6 } - 21 x ^ { 4 } + 4$ 
A)  $4 x ^ { 6 } - 21 x ^ { 4 } + 20$ 
B)  $4 x ^ { 6 } - 4 x ^ { 4 } + 4$ 
C)  $3 x ^ { 10 }$ 
D)  $4 x ^ { 6 } - 21 x ^ { 4 } + 4$ A

Question 2

Evaluate the polynomial for the given values of x and y.
-$2 y ^ { 2 } - 4 x y ; x = - 7$ and $y = 1$

Accepted Answer

A)  37 
B)  30 
C)  127 
D)  126 
A)  37 
B)  30 
C)  127 
D)  126 B

Question 3

Solve the problem.
-The area of the rectangle below is (z + 4)(4z + 3). Find another expression for this area by finding the sum of the areas of the smaller rectangles.

Accepted Answer

A)  $4 z ^ { 2 } + 3 z + 12$ 
B)  $4 z ^ { 2 } + 19 z$ 
C)  $4 z ^ { 2 } + 19 z + 12$ 
D)  $4 z ^ { 2 } + 16 z + 12$ 
A)  $4 z ^ { 2 } + 3 z + 12$ 
B)  $4 z ^ { 2 } + 19 z$ 
C)  $4 z ^ { 2 } + 19 z + 12$ 
D)  $4 z ^ { 2 } + 16 z + 12$ C

Question 4

Add the polynomials.
-$\left( - \frac { 1 } { 5 } x ^ { 2 } - \frac { 1 } { 4 } x - \frac { 1 } { 4 } \right) + \left( - \frac { 1 } { 3 } x ^ { 2 } - \frac { 1 } { 2 } x - \frac { 1 } { 4 } \right)$

Accepted Answer

A)  $- \frac { 8 } { 15 } x ^ { 4 } - \frac { 3 } { 4 } x ^ { 2 } - \frac { 1 } { 2 }$ 
B)  $- \frac { 77 } { 60 } x ^ { 6 } - \frac { 1 } { 2 }$ 
C)  $\frac { 2 } { 3 } x ^ { 2 } + \frac { 5 } { 4 } x + \frac { 5 } { 8 }$ 
D)  $- \frac { 8 } { 15 } x ^ { 2 } - \frac { 3 } { 4 } x - \frac { 1 } { 2 }$ 
A)  $- \frac { 8 } { 15 } x ^ { 4 } - \frac { 3 } { 4 } x ^ { 2 } - \frac { 1 } { 2 }$ 
B)  $- \frac { 77 } { 60 } x ^ { 6 } - \frac { 1 } { 2 }$ 
C)  $\frac { 2 } { 3 } x ^ { 2 } + \frac { 5 } { 4 } x + \frac { 5 } { 8 }$ 
D)  $- \frac { 8 } { 15 } x ^ { 2 } - \frac { 3 } { 4 } x - \frac { 1 } { 2 }$

Question 5

Use a vertical format to add the polynomials.
-$$\begin{array} { r r } 
1.5 x ^ { 3 } + 7.7 x ^ { 2 } + & 4.1 \
&- 3.4 x - 2.7 \
- 3.5 x ^ { 2 } + & x + 9.7 \
\hline
\end{array}$$

Accepted Answer

A)  $1.5 x ^ { 3 } + 11.2 x ^ { 2 } + 5.4 x - 8.3$ 
B)  $13.1 x ^ { 6 } + 11.1$ 
C)  $1.5 \mathrm { x } ^ { 3 } + 4.2 \mathrm { x } ^ { 2 } + 6.4 \mathrm { x } + 11.1$ 
D)  $1.5 \mathrm { x } ^ { 3 } + 4.2 \mathrm { x } ^ { 2 } + 7.4 \mathrm { x } + 11.1$ 
A)  $1.5 x ^ { 3 } + 11.2 x ^ { 2 } + 5.4 x - 8.3$ 
B)  $13.1 x ^ { 6 } + 11.1$ 
C)  $1.5 \mathrm { x } ^ { 3 } + 4.2 \mathrm { x } ^ { 2 } + 6.4 \mathrm { x } + 11.1$ 
D)  $1.5 \mathrm { x } ^ { 3 } + 4.2 \mathrm { x } ^ { 2 } + 7.4 \mathrm { x } + 11.1$

Question 6

Evaluate the polynomial for the given values of x and y.
-$x ^ { 3 } + 3 x ^ { 2 } y + 3 x y ^ { 2 } + y ^ { 3 } ; x = - 2$ and $y = - 3$

Accepted Answer

A)  $- 15$ 
B)  $- 125$ 
C)  25 
D)  $- 35$ 
A)  $- 15$ 
B)  $- 125$ 
C)  25 
D)  $- 35$

Question 7

Find the product.
-$- 7 x ( x - 8 )$

Accepted Answer

A)  $- 7 x ^ { 2 } + 56 x$ 
B)  $x ^ { 2 } + 56 x$ 
C)  $- 7 x ^ { 2 } - 8 x$ 
D)  $49 \mathrm { x } ^ { 2 }$ 
A)  $- 7 x ^ { 2 } + 56 x$ 
B)  $x ^ { 2 } + 56 x$ 
C)  $- 7 x ^ { 2 } - 8 x$ 
D)  $49 \mathrm { x } ^ { 2 }$

Question 8

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$( x + 1 ) ( x - 1 )$$

Accepted Answer

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

Question 9

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$( y - 4 ) ( y + 4 )$$

Accepted Answer

A)  $y ^ { 2 } - 8 y - 16$ 
B)  $y ^ { 2 } + 8 y - 16$ 
C)  $y ^ { 2 } - 8$ 
D)  $y ^ { 2 } - 16$ 
A)  $y ^ { 2 } - 8 y - 16$ 
B)  $y ^ { 2 } + 8 y - 16$ 
C)  $y ^ { 2 } - 8$ 
D)  $y ^ { 2 } - 16$

Question 10

Multiply by using the rule for the square of a binomial.
-$$\left( 11 x - \frac { 1 } { 11 } \right) ^ { 2 }$$

Accepted Answer

A)  $121 x ^ { 2 } - 2 x - \frac { 1 } { 121 }$ 
B)  $121 x ^ { 2 } - \frac { 1 } { 121 }$ 
C)  $121 x ^ { 2 } - 2 x + \frac { 1 } { 121 }$ 
D)  $121 x ^ { 2 } - \frac { 2 } { 11 } x + \frac { 1 } { 121 }$ 
A)  $121 x ^ { 2 } - 2 x - \frac { 1 } { 121 }$ 
B)  $121 x ^ { 2 } - \frac { 1 } { 121 }$ 
C)  $121 x ^ { 2 } - 2 x + \frac { 1 } { 121 }$ 
D)  $121 x ^ { 2 } - \frac { 2 } { 11 } x + \frac { 1 } { 121 }$

Question 11

Simplify the expression using the products-to-powers rule.
-$$\left( 2 x ^ { 7 } \right) ^ { 3 }$$

Accepted Answer

A)  $2 x ^ { 21 }$ 
B)  $2 x ^ { 10 }$ 
C)  $8 x ^ { 21 }$ 
D)  $8 \mathrm { x } ^ { 10 }$ 
A)  $2 x ^ { 21 }$ 
B)  $2 x ^ { 10 }$ 
C)  $8 x ^ { 21 }$ 
D)  $8 \mathrm { x } ^ { 10 }$

Question 12

Use a vertical format to subtract the polynomials.
-$$\begin{array} { r } 
0.07 y ^ { 3 } - 0.09 y ^ { 2 } + 0.02 y \
- \left( 0.02 y ^ { 3 } - 0.07 y ^ { 2 } - \quad y \right) \
\hline
\end{array}$$

Accepted Answer

A)  $0.5 y ^ { 3 } - 0.16 y ^ { 2 } + 0.03 y$ 
B)  $0.05 \mathrm { y } ^ { 3 } - 0.02 \mathrm { y } ^ { 2 } + 1.02 \mathrm { y }$ 
C)  $0.5 y ^ { 3 } - 0.02 y ^ { 2 } + 0.01 y$ 
D)  $0.05 y ^ { 3 } - 0.16 y ^ { 2 } - 0.98 y$ 
A)  $0.5 y ^ { 3 } - 0.16 y ^ { 2 } + 0.03 y$ 
B)  $0.05 \mathrm { y } ^ { 3 } - 0.02 \mathrm { y } ^ { 2 } + 1.02 \mathrm { y }$ 
C)  $0.5 y ^ { 3 } - 0.02 y ^ { 2 } + 0.01 y$ 
D)  $0.05 y ^ { 3 } - 0.16 y ^ { 2 } - 0.98 y$

Question 13

Add the polynomials.
-$$\left( 5 x ^ { 6 } + 9 x ^ { 5 } - 3 \right) + \left( 7 x ^ { 6 } + 9 x ^ { 5 } + 4 \right)$$

Accepted Answer

A)  $12 + 18 x ^ { 6 } + 1 x ^ { 5 }$ 
B)  $12 x ^ { 6 } + 18 x ^ { 5 } + 1$ 
C)  $31 \mathrm { x } ^ { 11 }$ 
D)  $4 x ^ { 6 } + 14 x ^ { 5 } + 13$ 
A)  $12 + 18 x ^ { 6 } + 1 x ^ { 5 }$ 
B)  $12 x ^ { 6 } + 18 x ^ { 5 } + 1$ 
C)  $31 \mathrm { x } ^ { 11 }$ 
D)  $4 x ^ { 6 } + 14 x ^ { 5 } + 13$

Question 14

Subtract the polynomials.
-$\left( 18 y ^ { 4 } - 15 y ^ { 3 } \right) - \left( - 8 y ^ { 4 } - 19 y ^ { 3 } \right)$

Accepted Answer

A)  $26 y ^ { 4 } - 34 y ^ { 3 }$ 
B)  $30 y ^ { 7 }$ 
C)  $10 y ^ { 4 } - 34 y ^ { 3 }$ 
D)  $26 y ^ { 4 } + 4 y ^ { 3 }$ 
A)  $26 y ^ { 4 } - 34 y ^ { 3 }$ 
B)  $30 y ^ { 7 }$ 
C)  $10 y ^ { 4 } - 34 y ^ { 3 }$ 
D)  $26 y ^ { 4 } + 4 y ^ { 3 }$

Question 15

Subtract the polynomials.
-$$\left( 4 x ^ { 6 } - 15 x ^ { 5 } - 19 \right) - \left( 8 x ^ { 5 } + 2 x ^ { 6 } + 2 \right)$$

Accepted Answer

A)  $2 x ^ { 6 } - 23 x ^ { 5 } - 17$ 
B)  $2 x ^ { 6 } - 13 x ^ { 5 } - 17$ 
C)  $- 42 x ^ { 11 }$ 
D)  $2 x ^ { 6 } - 23 x ^ { 5 } - 21$ 
A)  $2 x ^ { 6 } - 23 x ^ { 5 } - 17$ 
B)  $2 x ^ { 6 } - 13 x ^ { 5 } - 17$ 
C)  $- 42 x ^ { 11 }$ 
D)  $2 x ^ { 6 } - 23 x ^ { 5 } - 21$

Question 16

Graph the equation. Find seven solutions in your table of values for the equation by using integers for x, starting with -3
and ending with 3.
-$$y = x ^ { 2 } - 3$$
$\begin{array} { r | r } 
x & x ^ { 2 } - 3 \
\hline - 3 & \
- 2 & \
- 1 & \
0 & \
1 & \
2 & \
3 &
\end{array}$

Accepted Answer

A)   
B)   
C)   
D)   
A)   
B)   
C)   
D)

Question 17

Simplify the expression using the power rule.
-$\left( 5 ^ { 6 } \right) ^ { 5 }$

Accepted Answer

A)  $5 ^ { 30 }$ 
B)  $25 ^ { 6 }$ 
C)  $25 ^ { 30 }$ 
D)  $5 ^ { 11 }$ 
A)  $5 ^ { 30 }$ 
B)  $25 ^ { 6 }$ 
C)  $25 ^ { 30 }$ 
D)  $5 ^ { 11 }$

Question 18

Use a vertical format to add the polynomials.
-$$\begin{array} { l } 
2 y ^ { 5 } + 9 y ^ { 2 } + 5 \
9 y ^ { 5 } - 4 y ^ { 2 } + 8 \
\hline
\end{array}$$

Accepted Answer

A)  $14 y ^ { 5 } - 2 y ^ { 2 } + 17$ 
B)  $11 y ^ { 5 } + 5 y ^ { 2 } + 13$ 
C)  $11 + 5 y ^ { 5 } + 13 y ^ { 2 }$ 
D)  $29 y ^ { 7 }$ 
A)  $14 y ^ { 5 } - 2 y ^ { 2 } + 17$ 
B)  $11 y ^ { 5 } + 5 y ^ { 2 } + 13$ 
C)  $11 + 5 y ^ { 5 } + 13 y ^ { 2 }$ 
D)  $29 y ^ { 7 }$

Question 19

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$\left( x ^ { 2 } + 5 \right) \left( x ^ { 2 } - 5 \right)$$

Accepted Answer

A)  $x ^ { 4 } - 25$ 
B)  $x ^ { 4 } - 10$ 
C)  $x ^ { 4 } + 10 x ^ { 2 } - 25$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } - 25$ 
A)  $x ^ { 4 } - 25$ 
B)  $x ^ { 4 } - 10$ 
C)  $x ^ { 4 } + 10 x ^ { 2 } - 25$ 
D)  $x ^ { 4 } - 10 x ^ { 2 } - 25$

Question 20

Use a vertical format to subtract the polynomials.
-$$\begin{array} { r } 
12 x ^ { 3 } + 6 x ^ { 2 } \
- \left( 16 x ^ { 3 } - 2 x ^ { 2 } \right) \
\hline
\end{array}$$

Accepted Answer

A)  $- 4 x ^ { 3 } + 8 x ^ { 2 }$ \end{tabular} 
B)  $28 x ^ { 3 } + 4 x ^ { 2 }$ 
C)  $- 4 x ^ { 3 } + 4 x ^ { 2 }$ 
D)  $28 x ^ { 3 } + 8 x ^ { 2 }$ 
A)  $- 4 x ^ { 3 } + 8 x ^ { 2 }$ \end{tabular} 
B)  $28 x ^ { 3 } + 4 x ^ { 2 }$ 
C)  $- 4 x ^ { 3 } + 4 x ^ { 2 }$ 
D)  $28 x ^ { 3 } + 8 x ^ { 2 }$

Subtract the polynomials. - $\left( 8 x ^ { 6 } - 8 x ^ { 4 } + 12 \right) - \left( 4 x ^ { 6 } + 13 x ^ { 4 } - 8 \right)$

Evaluate the polynomial for the given values of x and y. - $2 y ^ { 2 } - 4 x y ; x = - 7$ and $y = 1$

Solve the problem. -The area of the rectangle below is (z + 4)(4z + 3). Find another expression for this area by finding the sum of the areas of the smaller rectangles.

Add the polynomials. - $\left( - \frac { 1 } { 5 } x ^ { 2 } - \frac { 1 } { 4 } x - \frac { 1 } { 4 } \right) + \left( - \frac { 1 } { 3 } x ^ { 2 } - \frac { 1 } { 2 } x - \frac { 1 } { 4 } \right)$

Use a vertical format to add the polynomials. - 1.5+7.7+ 4.1 -3.4x-2.7 -3.5+ x+9.7

Evaluate the polynomial for the given values of x and y. - $x ^ { 3 } + 3 x ^ { 2 } y + 3 x y ^ { 2 } + y ^ { 3 } ; x = - 2$ and $y = - 3$

Find the product. - $- 7 x ( x - 8 )$

Multiply using the rule for finding the product of the sum and difference of two terms. - $( x + 1 ) ( x - 1 )$

Multiply using the rule for finding the product of the sum and difference of two terms. - $( y - 4 ) ( y + 4 )$

Multiply by using the rule for the square of a binomial. - $\left( 11 x - \frac { 1 } { 11 } \right) ^ { 2 }$

Simplify the expression using the products-to-powers rule. - $\left( 2 x ^ { 7 } \right) ^ { 3 }$

Use a vertical format to subtract the polynomials. - 0.07-0.09+0.02y - 0.02-0.07-y

Add the polynomials. - $\left( 5 x ^ { 6 } + 9 x ^ { 5 } - 3 \right) + \left( 7 x ^ { 6 } + 9 x ^ { 5 } + 4 \right)$

Subtract the polynomials. - $\left( 18 y ^ { 4 } - 15 y ^ { 3 } \right) - \left( - 8 y ^ { 4 } - 19 y ^ { 3 } \right)$

Subtract the polynomials. - $\left( 4 x ^ { 6 } - 15 x ^ { 5 } - 19 \right) - \left( 8 x ^ { 5 } + 2 x ^ { 6 } + 2 \right)$

Simplify the expression using the power rule. - $\left( 5 ^ { 6 } \right) ^ { 5 }$

Use a vertical format to add the polynomials. - 2+9+5 9-4+8

Multiply using the rule for finding the product of the sum and difference of two terms. - $\left( x ^ { 2 } + 5 \right) \left( x ^ { 2 } - 5 \right)$

Use a vertical format to subtract the polynomials. - 12+6 - 16-2

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Factoring Polynomials

Rational Expressions

Basics of Functions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 5: Exponents and Polynomials

Subtract the polynomials. - (8x6−8x4+12)−(4x6+13x4−8)\left( 8 x ^ { 6 } - 8 x ^ { 4 } + 12 \right) - \left( 4 x ^ { 6 } + 13 x ^ { 4 } - 8 \right)(8x6−8x4+12)−(4x6+13x4−8)

Evaluate the polynomial for the given values of x and y. - 2y2−4xy;x=−72 y ^ { 2 } - 4 x y ; x = - 72y2−4xy;x=−7 and y=1y = 1y=1

Solve the problem. -The area of the rectangle below is (z + 4)(4z + 3). Find another expression for this area by finding the sum of the areas of the smaller rectangles.

Add the polynomials. - (−15x2−14x−14)+(−13x2−12x−14)\left( - \frac { 1 } { 5 } x ^ { 2 } - \frac { 1 } { 4 } x - \frac { 1 } { 4 } \right) + \left( - \frac { 1 } { 3 } x ^ { 2 } - \frac { 1 } { 2 } x - \frac { 1 } { 4 } \right)(−51​x2−41​x−41​)+(−31​x2−21​x−41​)