Question 1

Multiply the expression using the product rule.
-$$x ^ { 7 } \cdot x ^ { 7 } \cdot x ^ { 8 }$$

Accepted Answer

A)  $x ^ { 57 }$ 
B)  $x ^ { 15 }$ 
C)  $x ^ { 14 }$ 
D)  $x ^ { 22 }$ 
A)  $x ^ { 57 }$ 
B)  $x ^ { 15 }$ 
C)  $x ^ { 14 }$ 
D)  $x ^ { 22 }$

Question 2

Find the product.
-$11 x ^ { 7 } \left( 5 x ^ { 7 } - 10 x ^ { 5 } - 11 \right)$

Accepted Answer

A)  $55 x ^ { 14 } - 110 x ^ { 12 } - 121 x ^ { 7 }$ 
B)  $55 \mathrm { x } ^ { 14 } - 110 \mathrm { x } ^ { 12 }$ 
C)  $55 x ^ { 7 } - 110 x ^ { 5 } - 121$ 
D)  $55 x ^ { 14 } - 10 x ^ { 5 } - 11$ 
A)  $55 x ^ { 14 } - 110 x ^ { 12 } - 121 x ^ { 7 }$ 
B)  $55 \mathrm { x } ^ { 14 } - 110 \mathrm { x } ^ { 12 }$ 
C)  $55 x ^ { 7 } - 110 x ^ { 5 } - 121$ 
D)  $55 x ^ { 14 } - 10 x ^ { 5 } - 11$

Question 3

Perform the indicated operations.
-The bar graph shows the median annual income for residents of a selected region of the United States, by level of education. The given polynomial models describe the median annual income for men, M, and for women, W, who have
Completed x years of education. $$\begin{array} { l } 
M = - 23 x ^ { 3 } + 1170 x ^ { 2 } - 13,808 x + 72,566 \
W = 8 x ^ { 3 } - 56 x ^ { 2 } + 511 x + 14,763
\end{array}$$ Find a mathematical model for M - W and use it to calculate the difference in the median annual income between
Men and women with 10 years of education. Does the model underestimate or overestimate the actual
Difference?

Accepted Answer

A)  $16,433; overestimates 
B)  $4987; underestimates 
C)  $6213; underestimates 
D)  $9653; overestimates 
A)  $16,433; overestimates 
B)  $4987; underestimates 
C)  $6213; underestimates 
D)  $9653; overestimates

Question 4

Use a vertical format to subtract the polynomials.
-$$\begin{array} { r } 
9 y ^ { 6 } + 5 y ^ { 4 } + 3 y \
- \left( 2 y ^ { 6 } - 18 y ^ { 4 } + 9 y \right) \
\hline
\end{array}$$

Accepted Answer

A)  $7 y ^ { 6 } + 7 y ^ { 4 } - 6 y$ 
B)  $7 y ^ { 6 } + 7 y ^ { 4 } + 12 y$ 
C)  $7 y ^ { 6 } + 23 y ^ { 4 } - 6 y$ 
D)  $7 y ^ { 6 } + 23 y ^ { 4 } + 12 y$ 
A)  $7 y ^ { 6 } + 7 y ^ { 4 } - 6 y$ 
B)  $7 y ^ { 6 } + 7 y ^ { 4 } + 12 y$ 
C)  $7 y ^ { 6 } + 23 y ^ { 4 } - 6 y$ 
D)  $7 y ^ { 6 } + 23 y ^ { 4 } + 12 y$

Question 5

Add the polynomials.
-$\left( 6 x ^ { 2 } - 3 x + 8 \right) + \left( 3 x ^ { 2 } - 3 x - 2 \right)$

Accepted Answer

A)  $9 x ^ { 4 } - 6 x ^ { 2 } + 6$ 
B)  $9 x ^ { 2 } - 3 x + 6$ 
C)  $18 x ^ { 2 } - 3 x + 6$ 
D)  $9 x ^ { 2 } - 6 x + 6$ 
A)  $9 x ^ { 4 } - 6 x ^ { 2 } + 6$ 
B)  $9 x ^ { 2 } - 3 x + 6$ 
C)  $18 x ^ { 2 } - 3 x + 6$ 
D)  $9 x ^ { 2 } - 6 x + 6$

Question 6

Multiply by using the rule for the square of a binomial.
-$$\left( x ^ { 3 } + 14 \right) ^ { 2 }$$

Accepted Answer

A)  $196 x ^ { 6 } + 28 x ^ { 3 } + 196$ 
B)  $x ^ { 6 } + 196$ 
C)  $x ^ { 3 } + 196$ 
D)  $x ^ { 6 } + 28 x ^ { 3 } + 196$ 
A)  $196 x ^ { 6 } + 28 x ^ { 3 } + 196$ 
B)  $x ^ { 6 } + 196$ 
C)  $x ^ { 3 } + 196$ 
D)  $x ^ { 6 } + 28 x ^ { 3 } + 196$

Question 7

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.
-$$y = 4 - x ^ { 2 }$$
$\begin{array} { r | l } 
x & 4 - x ^ { 2 } \
\hline - 3 & \
- 2 & \
- 1 & \
0 & \
1 & \
2 & \
3 &
\end{array}$

Accepted Answer

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

Question 8

Multiply the expression using the product rule.
-$$4 ^ { 8 } \cdot 4 ^ { 6 }$$

Accepted Answer

A)  $16 ^ { 48 }$ 
B)  $4 ^ { 48 }$ 
C)  $16 ^ { 14 }$ 
D)  $4 ^ { 14 }$ 
A)  $16 ^ { 48 }$ 
B)  $4 ^ { 48 }$ 
C)  $16 ^ { 14 }$ 
D)  $4 ^ { 14 }$

Question 9

Use the FOIL method to find the product. Express the product in descending powers of the variable.
-$$\left( 4 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } - 9 \right)$$

Accepted Answer

A)  $12 x ^ { 4 } - 33 x ^ { 2 } - 9$ 
B)  $7 x ^ { 4 } - 33 x ^ { 2 } - 33$ 
C)  $7 x ^ { 4 } - 33 x ^ { 2 } - 9$ 
D)  $12 x ^ { 4 } - 33 x ^ { 2 } - 33$ 
A)  $12 x ^ { 4 } - 33 x ^ { 2 } - 9$ 
B)  $7 x ^ { 4 } - 33 x ^ { 2 } - 33$ 
C)  $7 x ^ { 4 } - 33 x ^ { 2 } - 9$ 
D)  $12 x ^ { 4 } - 33 x ^ { 2 } - 33$

Question 10

Evaluate the polynomial for the given values of x and y.
-$4 x + 9 y - 3 ; x = - 8$ and $y = - 6$

Accepted Answer

A)  $- 98$ 
B)  $- 86$ 
C)  $- 89$ 
D)  $- 93$ 
A)  $- 98$ 
B)  $- 86$ 
C)  $- 89$ 
D)  $- 93$

Question 11

Find the area of the shaded region. Write the answer as a polynomial in descending powers of x.
-

Accepted Answer

A)  $121 x ^ { 2 } - 3 x - 100$ 
B)  $118 x ^ { 2 } + 100$ 
C)  $118 x ^ { 2 } - 100$ 
D)  $124 x ^ { 2 } - 100$ 
A)  $121 x ^ { 2 } - 3 x - 100$ 
B)  $118 x ^ { 2 } + 100$ 
C)  $118 x ^ { 2 } - 100$ 
D)  $124 x ^ { 2 } - 100$

Question 12

Use the FOIL method to find the product. Express the product in descending powers of the variable.
-$$( 4 - 2 x ) ( 3 - 2 x )$$

Accepted Answer

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

Question 13

Add the polynomials.
-$$( 5 y + 3 ) + ( 2 y + 14 )$$

Accepted Answer

A)  $7 y ^ { 2 } + 17$ 
B)  $7 y + 17$ 
C)  $10 y ^ { 2 } + 42$ 
D)  $7 y - 17$ 
A)  $7 y ^ { 2 } + 17$ 
B)  $7 y + 17$ 
C)  $10 y ^ { 2 } + 42$ 
D)  $7 y - 17$

Question 14

Multiply the expression using the product rule.
-$y ^ { 10 } \cdot y ^ { 2 }$

Accepted Answer

A)  $y ^ { 20 }$ 
B)  $2 y ^ { 20 }$ 
C)  $\mathrm { y } ^ { 12 }$ 
D)  $2 \mathrm { y } ^ { 12 }$ 
A)  $y ^ { 20 }$ 
B)  $2 y ^ { 20 }$ 
C)  $\mathrm { y } ^ { 12 }$ 
D)  $2 \mathrm { y } ^ { 12 }$

Question 15

Use the FOIL method to find the product. Express the product in descending powers of the variable.
-$( x - 6 ) \left( x ^ { 2 } + 2 \right)$

Accepted Answer

A)  $x ^ { 3 } - 6 x ^ { 2 } + 2 x - 12$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } - 6 x - 12$ 
C)  $- 6 x ^ { 2 } + x - 12$ 
D)  $x ^ { 2 } - 4 x - 12$ 
A)  $x ^ { 3 } - 6 x ^ { 2 } + 2 x - 12$ 
B)  $x ^ { 3 } + 2 x ^ { 2 } - 6 x - 12$ 
C)  $- 6 x ^ { 2 } + x - 12$ 
D)  $x ^ { 2 } - 4 x - 12$

Question 16

Multiply the monomials.
-$\left( \frac { 1 } { 8 } x ^ { 3 } \right) \left( - \frac { 1 } { 3 } x ^ { 8 } \right)$

Accepted Answer

A)  $= \frac { 1 } { 24 } x ^ { 24 }$ 
B)  $= \frac { 1 } { 24 } x ^ { 11 }$ 
C)  $\frac { 1 } { 24 } x ^ { 24 }$ 
D)  $\frac { 1 } { 24 } x ^ { 11 }$ 
A)  $= \frac { 1 } { 24 } x ^ { 24 }$ 
B)  $= \frac { 1 } { 24 } x ^ { 11 }$ 
C)  $\frac { 1 } { 24 } x ^ { 24 }$ 
D)  $\frac { 1 } { 24 } x ^ { 11 }$

Question 17

Use a vertical format to find the product.
-$$\begin{array} { r } 
4 y ^ { 2 } - 2 y + 4 \
2 y - 3\
\hline 
\end{array}$$

Accepted Answer

A)  $- 4 y ^ { 3 } + 2 y ^ { 2 } - 4 y$ 
B)  $8 y ^ { 3 } - 16 y ^ { 2 } + 14 y - 12$ 
C)  $8 y ^ { 3 } + 8 y ^ { 2 } + 2 y - 12$ 
D)  $- 4 y ^ { 3 } - 10 y ^ { 2 } + 4 y$ 
A)  $- 4 y ^ { 3 } + 2 y ^ { 2 } - 4 y$ 
B)  $8 y ^ { 3 } - 16 y ^ { 2 } + 14 y - 12$ 
C)  $8 y ^ { 3 } + 8 y ^ { 2 } + 2 y - 12$ 
D)  $- 4 y ^ { 3 } - 10 y ^ { 2 } + 4 y$

Question 18

Use a vertical format to find the product.
-$$\begin{array} { r } 
4 x ^ { 3 } - 5 x ^ { 2 } + 6 x - 8 \
4 x - 2\
\hline 
\end{array}$$

Accepted Answer

A)  $8 x ^ { 4 } - 10 x ^ { 3 } + 12 x ^ { 2 } - 16 x$ 
B)  $8 x ^ { 4 } - 30 x ^ { 3 } + 36 x ^ { 2 } - 48 x$ 
C)  $16 x ^ { 4 } - 12 x ^ { 3 } + 34 x ^ { 2 } - 20 x - 16$ 
D)  $16 x ^ { 4 } - 28 x ^ { 3 } + 34 x ^ { 2 } - 44 x + 16$ 
A)  $8 x ^ { 4 } - 10 x ^ { 3 } + 12 x ^ { 2 } - 16 x$ 
B)  $8 x ^ { 4 } - 30 x ^ { 3 } + 36 x ^ { 2 } - 48 x$ 
C)  $16 x ^ { 4 } - 12 x ^ { 3 } + 34 x ^ { 2 } - 20 x - 16$ 
D)  $16 x ^ { 4 } - 28 x ^ { 3 } + 34 x ^ { 2 } - 44 x + 16$

Question 19

Subtract the polynomials.
-$\left( y ^ { 6 } - y ^ { 2 } \right) - \left( y ^ { 4 } - y \right)$

Accepted Answer

A)  $y ^ { 6 } - y ^ { 4 } - y ^ { 2 } + y$ 
B)  $y ^ { 6 } - y ^ { 2 } + y ^ { 4 } + y$ 
C)  $y ^ { 6 } - y ^ { 4 } - y ^ { 2 } - y$ 
D)  $y ^ { 6 } - y ^ { 4 } + y ^ { 2 } - y$ 
A)  $y ^ { 6 } - y ^ { 4 } - y ^ { 2 } + y$ 
B)  $y ^ { 6 } - y ^ { 2 } + y ^ { 4 } + y$ 
C)  $y ^ { 6 } - y ^ { 4 } - y ^ { 2 } - y$ 
D)  $y ^ { 6 } - y ^ { 4 } + y ^ { 2 } - y$

Question 20

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.
-A census was taken to determine the median annual income for residents of a selected region of the United States, by level of education. The given polynomial models describe the median annual income for men, M, and
For women, W, who have completed x years of education. Shown in a rectangular coordinate system are the
Graphs of the polynomial models. Identify the median annual income for a woman with 13 years of education as
A point on the appropriate graph. $$\begin{array} { l } 
M = 224 x ^ { 2 } - 1266 x + 20,106 \
W = 287 x ^ { 2 } - 4030 x + 33,761
\end{array}$$

Accepted Answer

A)  (13, 41,504) 
B)  (13, 56,696) 
C)  (13, 29,874) 
D)  (13, 78,234) 
A)  (13, 41,504) 
B)  (13, 56,696) 
C)  (13, 29,874) 
D)  (13, 78,234)

Multiply the expression using the product rule. - $x ^ { 7 } \cdot x ^ { 7 } \cdot x ^ { 8 }$

Find the product. - $11 x ^ { 7 } \left( 5 x ^ { 7 } - 10 x ^ { 5 } - 11 \right)$

Use a vertical format to subtract the polynomials. - 9+5+3y - 2-18+9y

Add the polynomials. - $\left( 6 x ^ { 2 } - 3 x + 8 \right) + \left( 3 x ^ { 2 } - 3 x - 2 \right)$

Multiply by using the rule for the square of a binomial. - $\left( x ^ { 3 } + 14 \right) ^ { 2 }$

Multiply the expression using the product rule. - $4 ^ { 8 } \cdot 4 ^ { 6 }$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $\left( 4 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } - 9 \right)$

Evaluate the polynomial for the given values of x and y. - $4 x + 9 y - 3 ; x = - 8$ and $y = - 6$

Find the area of the shaded region. Write the answer as a polynomial in descending powers of x. -

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( 4 - 2 x ) ( 3 - 2 x )$

Add the polynomials. - $( 5 y + 3 ) + ( 2 y + 14 )$

Multiply the expression using the product rule. - $y ^ { 10 } \cdot y ^ { 2 }$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( x - 6 ) \left( x ^ { 2 } + 2 \right)$

Multiply the monomials. - $\left( \frac { 1 } { 8 } x ^ { 3 } \right) \left( - \frac { 1 } { 3 } x ^ { 8 } \right)$

Use a vertical format to find the product. - 4-2y+4 2y-3

Use a vertical format to find the product. - 4-5+6x-8 4x-2

Subtract the polynomials. - $\left( y ^ { 6 } - y ^ { 2 } \right) - \left( y ^ { 4 } - y \right)$

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

Multiply the expression using the product rule. - x7⋅x7⋅x8x ^ { 7 } \cdot x ^ { 7 } \cdot x ^ { 8 }x7⋅x7⋅x8

Find the product. - 11x7(5x7−10x5−11)11 x ^ { 7 } \left( 5 x ^ { 7 } - 10 x ^ { 5 } - 11 \right)11x7(5x7−10x5−11)

Use a vertical format to subtract the polynomials. - 9+5+3y - 2-18+9y

Add the polynomials. - (6x2−3x+8)+(3x2−3x−2)\left( 6 x ^ { 2 } - 3 x + 8 \right) + \left( 3 x ^ { 2 } - 3 x - 2 \right)(6x2−3x+8)+(3x2−3x−2)

Multiply by using the rule for the square of a binomial. - (x3+14)2\left( x ^ { 3 } + 14 \right) ^ { 2 }(x3+14)2

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=4−x2y = 4 - x ^ { 2 }y=4−x2 x 4- -3 -2 -1 0 1 2 3

Multiply the expression using the product rule. - 48⋅464 ^ { 8 } \cdot 4 ^ { 6 }48⋅46

Use the FOIL method to find the product. Express the product in descending powers of the variable. - (4x2+1)(3x2−9)\left( 4 x ^ { 2 } + 1 \right) \left( 3 x ^ { 2 } - 9 \right)(4x2+1)(3x2−9)

Evaluate the polynomial for the given values of x and y. - 4x+9y−3;x=−84 x + 9 y - 3 ; x = - 84x+9y−3;x=−8 and y=−6y = - 6y=−6