Question 1

Multiply the monomials.
-$$\left( - \frac { 1 } { 8 } x ^ { 9 } \right) \left( - \frac { 1 } { 9 } x ^ { 8 } \right)$$

Accepted Answer

A)  $\frac { 1 } { 72 } x ^ { 72 }$ 
B)  $\frac { 1 } { 72 } x ^ { 17 }$ 
C)  $=- \frac { 1 } { 72 } x ^ { 72 }$ 
D)  $=- \frac { 1 } { 72 } x ^ { 17 }$ 
A)  $\frac { 1 } { 72 } x ^ { 72 }$ 
B)  $\frac { 1 } { 72 } x ^ { 17 }$ 
C)  $=- \frac { 1 } { 72 } x ^ { 72 }$ 
D)  $=- \frac { 1 } { 72 } x ^ { 17 }$

Question 2

Use a vertical format to subtract the polynomials.
-$$\begin{array} { r } 
5 x ^ { 6 } + 3 x ^ { 5 } + 2 x ^ { 4 } - 6 \
- \left( 2 x ^ { 6 } - 7 x ^ { 5 } + 4 x ^ { 4 } - 5 \right) \
\hline
\end{array}$$

Accepted Answer

A)  $3 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 11$ 
B)  $7 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 11$ 
C)  $7 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 1$ 
D)  $3 x ^ { 6 } + 10 x ^ { 5 } - 2 x ^ { 4 } - 1$ 
A)  $3 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 11$ 
B)  $7 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 11$ 
C)  $7 x ^ { 6 } - 4 x ^ { 5 } + 6 x ^ { 4 } - 1$ 
D)  $3 x ^ { 6 } + 10 x ^ { 5 } - 2 x ^ { 4 } - 1$

Question 3

Perform the indicated operations.
-Subtract -6 - 2x7 + 5x8 - 9x6 + 9x from the sum of -4x6 + 9x + 9 and 9x8 + 4x7.

Accepted Answer

A)  4x8 + 6x7 + 5x6 + 15 
B)  14x8 + 2x7 - 13x6 + 15 
C)  14x8 + 2x7 - 13x6 + 3 
D)  4x8 + 2x7 - 13x6 + 3 
A)  4x8 + 6x7 + 5x6 + 15 
B)  14x8 + 2x7 - 13x6 + 15 
C)  14x8 + 2x7 - 13x6 + 3 
D)  4x8 + 2x7 - 13x6 + 3

Question 4

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

Accepted Answer

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

Question 5

Find the area of the shaded region. Write the answer as a polynomial in descending powers of x.
-The square garden in the figure measures x yards on each side. The garden is to be expanded so that one side (the top of the figure) is increased by 3 yards and the adjacent side (the right side of the figure) is increased by 1
Yard. Write a polynomial in descending powers of x that expresses the area of the larger garden. Then use the
Polynomial to determine the area of the larger garden if the original garden measures 8 yards on a side.

Accepted Answer

A)  $x ^ { 2 } + 4 ; 68$ square yards 
B)  $x ^ { 2 } + 4 ; 99$ square yards 
C)  $x ^ { 2 } + 4 x + 3 ; 68$ square yards 
D)  $x ^ { 2 } + 4 x + 3 ; 99$ square yards 
A)  $x ^ { 2 } + 4 ; 68$ square yards 
B)  $x ^ { 2 } + 4 ; 99$ square yards 
C)  $x ^ { 2 } + 4 x + 3 ; 68$ square yards 
D)  $x ^ { 2 } + 4 x + 3 ; 99$ square yards

Question 6

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$( 7 + r ) ( 7 - r )$$

Accepted Answer

A)  $49 - 14 r - r ^ { 2 }$ 
B)  $14 - r ^ { 2 }$ 
C)  $49 + 14 r - r ^ { 2 }$ 
D)  $49 - r ^ { 2 }$ 
A)  $49 - 14 r - r ^ { 2 }$ 
B)  $14 - r ^ { 2 }$ 
C)  $49 + 14 r - r ^ { 2 }$ 
D)  $49 - r ^ { 2 }$

Question 7

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

Accepted Answer

A)  $x ^ { 3 }$ 
B)  $2 x ^ { 2 }$ 
C)  $2 x ^ { 3 }$ 
D)  $x ^ { 2 }$ 
A)  $x ^ { 3 }$ 
B)  $2 x ^ { 2 }$ 
C)  $2 x ^ { 3 }$ 
D)  $x ^ { 2 }$

Question 8

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

Accepted Answer

A)  $9 x ^ { 2 } + 36 x - 36$ 
B)  $9 x ^ { 2 } - 36 x + 36$ 
C)  $9 x ^ { 2 } - 36 x - 36$ 
D)  $9 x ^ { 2 } + 36 x + 36$ 
A)  $9 x ^ { 2 } + 36 x - 36$ 
B)  $9 x ^ { 2 } - 36 x + 36$ 
C)  $9 x ^ { 2 } - 36 x - 36$ 
D)  $9 x ^ { 2 } + 36 x + 36$

Question 9

Multiply by using the rule for the square of a binomial.
-$$( 3 x + 4 ) ^ { 2 }$$

Accepted Answer

A)  $3 x ^ { 2 } + 16$ 
B)  $9 x ^ { 2 } + 16$ 
C)  $3 x ^ { 2 } + 24 x + 16$ 
D)  $9 x ^ { 2 } + 24 x + 16$ 
A)  $3 x ^ { 2 } + 16$ 
B)  $9 x ^ { 2 } + 16$ 
C)  $3 x ^ { 2 } + 24 x + 16$ 
D)  $9 x ^ { 2 } + 24 x + 16$

Question 10

Multiply the monomials.
-$$\left( - 8 x ^ { 9 } \right) \left( - 3 x ^ { 2 } \right)$$

Accepted Answer

A)  $- 24 x ^ { 18 }$ 
B)  $24 \mathrm { x } ^ { 11 }$ 
C)  $- 24 x ^ { 11}$ 
D)  $24 \mathrm { x } ^ { 18 }$ 
A)  $- 24 x ^ { 18 }$ 
B)  $24 \mathrm { x } ^ { 11 }$ 
C)  $- 24 x ^ { 11}$ 
D)  $24 \mathrm { x } ^ { 18 }$

Question 11

Find the product.
-$$6 x ^ { 5 } ( 2 x + 8 )$$

Accepted Answer

A)  $12 x ^ { 6 } + 48 x ^ { 5 }$ 
B)  $12 x + 48$ 
C)  $60 x ^ { 5 }$ 
D)  $12 x ^ { 6 } + 8$ 
A)  $12 x ^ { 6 } + 48 x ^ { 5 }$ 
B)  $12 x + 48$ 
C)  $60 x ^ { 5 }$ 
D)  $12 x ^ { 6 } + 8$

Question 12

Use a vertical format to find the product.
-$$\begin{array} { r } 
6 x ^ { 2 } + 7 x + 8 \
x + 5 \
\hline
\end{array}$$

Accepted Answer

A)  $36 x ^ { 3 } + 42 x ^ { 2 } + 48 x$ 
B)  $6 x ^ { 3 } + 30 x ^ { 2 } + 35 x + 40$ 
C)  $6 x ^ { 3 } + 37 x ^ { 2 } + 43 x + 40$ 
D)  $36 x ^ { 3 } + 30 x ^ { 2 } + 35 x + 13$ 
A)  $36 x ^ { 3 } + 42 x ^ { 2 } + 48 x$ 
B)  $6 x ^ { 3 } + 30 x ^ { 2 } + 35 x + 40$ 
C)  $6 x ^ { 3 } + 37 x ^ { 2 } + 43 x + 40$ 
D)  $36 x ^ { 3 } + 30 x ^ { 2 } + 35 x + 13$

Question 13

Simplify the expression using the products-to-powers rule.
-$\left( - 3 x ^ { 2 } \right) ^ { 4 }$

Accepted Answer

A)  $- 3 x ^ { 8 }$ 
B)  $- 81 x ^ { 8 }$ 
C)  $81 x ^ { 6 }$ 
D)  $81 x ^ { 8 }$ 
A)  $- 3 x ^ { 8 }$ 
B)  $- 81 x ^ { 8 }$ 
C)  $81 x ^ { 6 }$ 
D)  $81 x ^ { 8 }$

Question 14

Use the FOIL method to find the product. Express the product in descending powers of the variable.
-$$( x + 12 ) ( x + 5 )$$

Accepted Answer

A)  $x ^ { 2 } + 16 x + 60$ 
B)  $x ^ { 2 } + 60 x + 17$ 
C)  $x ^ { 2 } + 17 x + 16$ 
D)  $x ^ { 2 } + 17 x + 60$ 
A)  $x ^ { 2 } + 16 x + 60$ 
B)  $x ^ { 2 } + 60 x + 17$ 
C)  $x ^ { 2 } + 17 x + 16$ 
D)  $x ^ { 2 } + 17 x + 60$

Question 15

Perform the indicated operations.
-$\left[ \left( 1.1 x ^ { 3 } + 7.9 x ^ { 2 } + 4.2 \right) + ( 6.2 x - 2.3 ) \right] - \left( 3.7 x ^ { 2 } - x - 9.9 \right)$

Accepted Answer

A)  $1.1 x ^ { 3 } + 4.2 x ^ { 2 } + 6.2 x + 11.8$ 
B)  $12.5 x ^ { 6 } + 11.8$ 
C)  $1.1 x ^ { 3 } + 11.6 x ^ { 2 } + 5.2 x - 8$ 
D)  $1.1 x ^ { 3 } + 4.2 x ^ { 2 } + 7.2 x + 11.8$ 
A)  $1.1 x ^ { 3 } + 4.2 x ^ { 2 } + 6.2 x + 11.8$ 
B)  $12.5 x ^ { 6 } + 11.8$ 
C)  $1.1 x ^ { 3 } + 11.6 x ^ { 2 } + 5.2 x - 8$ 
D)  $1.1 x ^ { 3 } + 4.2 x ^ { 2 } + 7.2 x + 11.8$

Question 16

Simplify the expression using the products-to-powers rule.
-$$\left( - 3 x ^ { 6 } \right) ^ { 3 }$$

Accepted Answer

A)  $- 3 x ^ { 18 }$ 
B)  $- 27 x ^ { 18 }$ 
C)  $27 x ^ { 18 }$ 
D)  $- 27 x ^ { 9 }$ 
A)  $- 3 x ^ { 18 }$ 
B)  $- 27 x ^ { 18 }$ 
C)  $27 x ^ { 18 }$ 
D)  $- 27 x ^ { 9 }$

Question 17

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

Accepted Answer

A)  $28 x ^ { 2 } - 30 x - 100$ 
B)  $28 x ^ { 2 } + 110 x - 100$ 
C)  $28 x ^ { 2 } - 30 x + 100$ 
D)  $28 x ^ { 2 } - 70 x - 100$ 
A)  $28 x ^ { 2 } - 30 x - 100$ 
B)  $28 x ^ { 2 } + 110 x - 100$ 
C)  $28 x ^ { 2 } - 30 x + 100$ 
D)  $28 x ^ { 2 } - 70 x - 100$

Question 18

Use a vertical format to add the polynomials.
-$$\begin{array} { l } 
- \frac { 1 } { 5 } x ^ { 2 } + \frac { 2 } { 3 } x + \frac { 2 } { 5 } \
- \frac { 3 } { 5 } x ^ { 2 } + \frac { 3 } { 4 } x - \frac { 1 } { 3 } \
\hline
\end{array}$$

Accepted Answer

A)  $- \frac { 4 } { 5 } x ^ { 2 } + \frac { 17 } { 12 } x + \frac { 1 } { 15 }$ 
B)  $- \frac { 4 } { 5 } x ^ { 4 } + \frac { 17 } { 12 } x ^ { 2 } + \frac { 1 } { 15 }$ 
C)  $\frac { 6 } { 5 } x ^ { 2 } + 5 x - \frac { 4 } { 3 }$ 
D)  $\frac { 37 } { 60 } x ^ { 6 } + \frac { 1 } { 15 }$ 
A)  $- \frac { 4 } { 5 } x ^ { 2 } + \frac { 17 } { 12 } x + \frac { 1 } { 15 }$ 
B)  $- \frac { 4 } { 5 } x ^ { 4 } + \frac { 17 } { 12 } x ^ { 2 } + \frac { 1 } { 15 }$ 
C)  $\frac { 6 } { 5 } x ^ { 2 } + 5 x - \frac { 4 } { 3 }$ 
D)  $\frac { 37 } { 60 } x ^ { 6 } + \frac { 1 } { 15 }$

Question 19

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$\left( 3 x + \frac { 1 } { 3 } \right) \left( 3 x - \frac { 1 } { 3 } \right)$$

Accepted Answer

A)  $9 x ^ { 2 } - \frac { 2 } { 3 } x + \frac { 1 } { 9 }$ 
B)  $9 x ^ { 2 } - \frac { 2 } { 3 }$ 
C)  $9 x ^ { 2 } - \frac { 2 } { 3 } x - \frac { 1 } { 9 }$ 
D)  $9 x ^ { 2 } - \frac { 1 } { 9 }$ 
A)  $9 x ^ { 2 } - \frac { 2 } { 3 } x + \frac { 1 } { 9 }$ 
B)  $9 x ^ { 2 } - \frac { 2 } { 3 }$ 
C)  $9 x ^ { 2 } - \frac { 2 } { 3 } x - \frac { 1 } { 9 }$ 
D)  $9 x ^ { 2 } - \frac { 1 } { 9 }$

Question 20

Multiply by using the rule for the square of a binomial.
-$$\left( 4 x ^ { 2 } - 7 \right) ^ { 2 }$$

Accepted Answer

A)  $16 x ^ { 4 } - 56 x ^ { 2 } + 49$ 
B)  $4 x ^ { 4 } - 56 x ^ { 2 } + 49$ 
C)  $16 x ^ { 4 } + 49$ 
D)  $4 x ^ { 4 } + 49$ 
A)  $16 x ^ { 4 } - 56 x ^ { 2 } + 49$ 
B)  $4 x ^ { 4 } - 56 x ^ { 2 } + 49$ 
C)  $16 x ^ { 4 } + 49$ 
D)  $4 x ^ { 4 } + 49$

Multiply the monomials. - $\left( - \frac { 1 } { 8 } x ^ { 9 } \right) \left( - \frac { 1 } { 9 } x ^ { 8 } \right)$

Use a vertical format to subtract the polynomials. - 5+3+2-6 - 2-7+4-5

Perform the indicated operations. -Subtract -6 - 2x7 + 5x8 - 9x6 + 9x from the sum of -4x6 + 9x + 9 and 9x8 + 4x7.

Multiply using the rule for finding the product of the sum and difference of two terms. - $( 7 + r ) ( 7 - r )$

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

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

Multiply by using the rule for the square of a binomial. - $( 3 x + 4 ) ^ { 2 }$

Multiply the monomials. - $\left( - 8 x ^ { 9 } \right) \left( - 3 x ^ { 2 } \right)$

Find the product. - $6 x ^ { 5 } ( 2 x + 8 )$

Use a vertical format to find the product. - 6+7x+8 x+5

Simplify the expression using the products-to-powers rule. - $\left( - 3 x ^ { 2 } \right) ^ { 4 }$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( x + 12 ) ( x + 5 )$

Perform the indicated operations. - $\left[ \left( 1.1 x ^ { 3 } + 7.9 x ^ { 2 } + 4.2 \right) + ( 6.2 x - 2.3 ) \right] - \left( 3.7 x ^ { 2 } - x - 9.9 \right)$

Simplify the expression using the products-to-powers rule. - $\left( - 3 x ^ { 6 } \right) ^ { 3 }$

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

Use a vertical format to add the polynomials. - -+x+ -+x-

Multiply using the rule for finding the product of the sum and difference of two terms. - $\left( 3 x + \frac { 1 } { 3 } \right) \left( 3 x - \frac { 1 } { 3 } \right)$

Multiply by using the rule for the square of a binomial. - $\left( 4 x ^ { 2 } - 7 \right) ^ { 2 }$

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

Multiply the monomials. - (−18x9)(−19x8)\left( - \frac { 1 } { 8 } x ^ { 9 } \right) \left( - \frac { 1 } { 9 } x ^ { 8 } \right)(−81​x9)(−91​x8)

Use a vertical format to subtract the polynomials. - 5+3+2-6 - 2-7+4-5

Perform the indicated operations. -Subtract -6 - 2x7 + 5x8 - 9x6 + 9x from the sum of -4x6 + 9x + 9 and 9x8 + 4x7.

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

Multiply using the rule for finding the product of the sum and difference of two terms. - (7+r)(7−r)( 7 + r ) ( 7 - r )(7+r)(7−r)

Multiply the expression using the product rule. - x⋅x2x \cdot x ^ { 2 }x⋅x2

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

Multiply by using the rule for the square of a binomial. - (3x+4)2( 3 x + 4 ) ^ { 2 }(3x+4)2

Multiply the monomials. - (−8x9)(−3x2)\left( - 8 x ^ { 9 } \right) \left( - 3 x ^ { 2 } \right)(−8x9)(−3x2)

Find the product. - 6x5(2x+8)6 x ^ { 5 } ( 2 x + 8 )6x5(2x+8)

Use a vertical format to find the product. - 6+7x+8 x+5

Simplify the expression using the products-to-powers rule. - (−3x2)4\left( - 3 x ^ { 2 } \right) ^ { 4 }(−3x2)4

Use the FOIL method to find the product. Express the product in descending powers of the variable. - (x+12)(x+5)( x + 12 ) ( x + 5 )(x+12)(x+5)

Perform the indicated operations. - [(1.1x3+7.9x2+4.2)+(6.2x−2.3)]−(3.7x2−x−9.9)\left[ \left( 1.1 x ^ { 3 } + 7.9 x ^ { 2 } + 4.2 \right) + ( 6.2 x - 2.3 ) \right] - \left( 3.7 x ^ { 2 } - x - 9.9 \right)[(1.1x3+7.9x2+4.2)+(6.2x−2.3)]−(3.7x2−x−9.9)

Simplify the expression using the products-to-powers rule. - (−3x6)3\left( - 3 x ^ { 6 } \right) ^ { 3 }(−3x6)3

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

Use a vertical format to add the polynomials. - -+x+ -+x-

Multiply using the rule for finding the product of the sum and difference of two terms. - (3x+13)(3x−13)\left( 3 x + \frac { 1 } { 3 } \right) \left( 3 x - \frac { 1 } { 3 } \right)(3x+31​)(3x−31​)

Multiply by using the rule for the square of a binomial. - (4x2−7)2\left( 4 x ^ { 2 } - 7 \right) ^ { 2 }(4x2−7)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

Multiply the monomials. - $\left( - \frac { 1 } { 8 } x ^ { 9 } \right) \left( - \frac { 1 } { 9 } x ^ { 8 } \right)$

Multiply using the rule for finding the product of the sum and difference of two terms. - $( 7 + r ) ( 7 - r )$

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

Multiply by using the rule for the square of a binomial. - $( 3 x + 4 ) ^ { 2 }$

Multiply the monomials. - $\left( - 8 x ^ { 9 } \right) \left( - 3 x ^ { 2 } \right)$

Find the product. - $6 x ^ { 5 } ( 2 x + 8 )$

Simplify the expression using the products-to-powers rule. - $\left( - 3 x ^ { 2 } \right) ^ { 4 }$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( x + 12 ) ( x + 5 )$

Perform the indicated operations. - $\left[ \left( 1.1 x ^ { 3 } + 7.9 x ^ { 2 } + 4.2 \right) + ( 6.2 x - 2.3 ) \right] - \left( 3.7 x ^ { 2 } - x - 9.9 \right)$

Simplify the expression using the products-to-powers rule. - $\left( - 3 x ^ { 6 } \right) ^ { 3 }$

Multiply using the rule for finding the product of the sum and difference of two terms. - $\left( 3 x + \frac { 1 } { 3 } \right) \left( 3 x - \frac { 1 } { 3 } \right)$

Multiply by using the rule for the square of a binomial. - $\left( 4 x ^ { 2 } - 7 \right) ^ { 2 }$