Question 1

Solve the problem.
-Find the area of a triangle with a base of 7x inches and a height of (10x + 4) inches.

Accepted Answer

A)  $\left( 17 x ^ { 2 } + 11 x \right)$ sq. in. 
B)  $\left( 35 x ^ { 2 } + 14 x \right)$ sq. in. 
C)  $\left( 70 x ^ { 2 } + 28 x \right)$ sq. in. 
D)  $( 35 x + 14 )$ sq. in. 
A)  $\left( 17 x ^ { 2 } + 11 x \right)$ sq. in. 
B)  $\left( 35 x ^ { 2 } + 14 x \right)$ sq. in. 
C)  $\left( 70 x ^ { 2 } + 28 x \right)$ sq. in. 
D)  $( 35 x + 14 )$ sq. in.

Question 2

Add the polynomials.
-$$\left( 9 x ^ { 3 } + 5 x + 7 \right) + \left( 8 x ^ { 2 } + 4 x + 5 \right)$$

Accepted Answer

A)  $17 x ^ { 3 } + 9 x + 12$ 
B)  $17 x ^ { 3 } + 13 x ^ { 2 } + 7 x + 5$ 
C)  $9 x ^ { 3 } + 13 x ^ { 2 } + 11 x + 5$ 
D)  $9 x ^ { 3 } + 8 x ^ { 2 } + 9 x + 12$ 
A)  $17 x ^ { 3 } + 9 x + 12$ 
B)  $17 x ^ { 3 } + 13 x ^ { 2 } + 7 x + 5$ 
C)  $9 x ^ { 3 } + 13 x ^ { 2 } + 11 x + 5$ 
D)  $9 x ^ { 3 } + 8 x ^ { 2 } + 9 x + 12$

Question 3

Multiply by using the rule for the square of a binomial.
-$$( 4 - 9 x ) ^ { 2 }$$

Accepted Answer

A)  $9 x ^ { 2 } - 16$ 
B)  $81 x ^ { 2 } - 72 x + 16$ 
C)  $81 x ^ { 2 } - 16$ 
D)  $9 x ^ { 2 } - 72 x + 16$ 
A)  $9 x ^ { 2 } - 16$ 
B)  $81 x ^ { 2 } - 72 x + 16$ 
C)  $81 x ^ { 2 } - 16$ 
D)  $9 x ^ { 2 } - 72 x + 16$

Question 4

Find the product.
-$( 9 x - 1 ) \left( x ^ { 2 } - 5 x + 1 \right)$

Accepted Answer

A)  $9 x ^ { 3 } - 44 x ^ { 2 } + 4 x - 1$ 
B)  $9 x ^ { 3 } + 46 x ^ { 2 } - 14 x + 1$ 
C)  $9 x ^ { 3 } - 46 x ^ { 2 } + 14 x - 1$ 
D)  $9 x ^ { 3 } - 45 x ^ { 2 } + 9 x + 1$ 
A)  $9 x ^ { 3 } - 44 x ^ { 2 } + 4 x - 1$ 
B)  $9 x ^ { 3 } + 46 x ^ { 2 } - 14 x + 1$ 
C)  $9 x ^ { 3 } - 46 x ^ { 2 } + 14 x - 1$ 
D)  $9 x ^ { 3 } - 45 x ^ { 2 } + 9 x + 1$

Question 5

Multiply the monomials.
-$\left( - \frac { 1 } { 5 } x ^ { 7 } \right) \left( \frac { 1 } { 4 } x ^ { 9 } \right)$

Accepted Answer

A)  $\frac { 1 } { 20 } x ^ { 16 }$ 
B)  $- \frac { 1 } { 20 } x ^ { 16 }$ 
C)  - \frac { 1 } { 20 } x ^ { 63 }\) 
D)  $\frac { 1 } { 20 } x ^ { 63 }$ 
A)  $\frac { 1 } { 20 } x ^ { 16 }$ 
B)  $- \frac { 1 } { 20 } x ^ { 16 }$ 
C)  - \frac { 1 } { 20 } x ^ { 63 }\) 
D)  $\frac { 1 } { 20 } x ^ { 63 }$

Question 6

Use a vertical format to add the polynomials.
-$$\begin{array} { r r } 
- 7 x ^ { 3 } & + 7 x - 6 \
5 x ^ { 2 } & + 8 x - 5 \
\hline
\end{array}$$

Accepted Answer

A)  $- 7 x ^ { 3 } + 12 x ^ { 2 } + 2 x - 5$ 
B)  $- 7 x ^ { 3 } + 5 x ^ { 2 } + 15 x - 11$ 
C)  $- 2 x ^ { 3 } + 15 x - 11$ 
D)  $- 2 x ^ { 3 } + 12 x ^ { 2 } - 6 x - 5$ 
A)  $- 7 x ^ { 3 } + 12 x ^ { 2 } + 2 x - 5$ 
B)  $- 7 x ^ { 3 } + 5 x ^ { 2 } + 15 x - 11$ 
C)  $- 2 x ^ { 3 } + 15 x - 11$ 
D)  $- 2 x ^ { 3 } + 12 x ^ { 2 } - 6 x - 5$

Question 7

Use a vertical format to add the polynomials.
-$$\begin{array} { r } 
9 y ^ { 5 } + 3 y ^ { 3 } \
3 y ^ { 5 } - 5 y ^ { 3 } \
\hline
\end{array}$$

Accepted Answer

A)  $10 y ^ { 8 }$ 
B)  $12 y ^ { 5 } - 2 y ^ { 3 }$ 
C)  $12 y ^ { 10 } - 2 y ^ { 6 }$ 
D)  $10 \mathrm { y } ^ { 16 }$ 
A)  $10 y ^ { 8 }$ 
B)  $12 y ^ { 5 } - 2 y ^ { 3 }$ 
C)  $12 y ^ { 10 } - 2 y ^ { 6 }$ 
D)  $10 \mathrm { y } ^ { 16 }$

Question 8

Simplify the expression using the power rule.
-$\left[ \left( - 7 ^ { 5 } \right) \right] ^ { 10 }$

Accepted Answer

A)  $( - 7 ) ^ { 50 }$ 
B)  $( - 49 ) ^ { 50 }$ 
C)  $( - 49 ) ^ { 5 }$ 
D)  $( - 7 ) ^{ 15 }$ 
A)  $( - 7 ) ^ { 50 }$ 
B)  $( - 49 ) ^ { 50 }$ 
C)  $( - 49 ) ^ { 5 }$ 
D)  $( - 7 ) ^{ 15 }$

Question 9

Find the product.
-$$- 6 x ^ { 4 } \left( 8 x ^ { 5 } + 7 \right)$$

Accepted Answer

A)  $- 48 x ^ { 5 } - 42$ 
B)  $- 48 x ^ { 9 } - 42 x ^ { 4 }$ 
C)  $- 48 x ^ { 9 } + 7$ 
D)  $- 90 x ^ { 4 }$ 
A)  $- 48 x ^ { 5 } - 42$ 
B)  $- 48 x ^ { 9 } - 42 x ^ { 4 }$ 
C)  $- 48 x ^ { 9 } + 7$ 
D)  $- 90 x ^ { 4 }$

Question 10

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
-$$19 y ^ { 9 }$$

Accepted Answer

A)  Binomial, degree 19 
B)  Binomial, degree 9 
C)  Monomial, degree 19 
D)  Monomial, degree 9 
A)  Binomial, degree 19 
B)  Binomial, degree 9 
C)  Monomial, degree 19 
D)  Monomial, degree 9

Question 11

Find the product.
-$$( x + 11 ) \left( x ^ { 3 } + 7 x - 8 \right)$$

Accepted Answer

A)  $x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 85 x + 88$ 
B)  $x ^ { 3 } + 18 x ^ { 2 } + 69 x - 88$ 
C)  $x ^ { 4 } + 7 x ^ { 2 } - 8 x + 11$ 
D)  $x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 69 x - 88$ 
A)  $x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 85 x + 88$ 
B)  $x ^ { 3 } + 18 x ^ { 2 } + 69 x - 88$ 
C)  $x ^ { 4 } + 7 x ^ { 2 } - 8 x + 11$ 
D)  $x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 69 x - 88$

Question 12

Subtract the polynomials.
-$$( 4 x - 7 ) - ( 20 x + 19 )$$

Accepted Answer

A)  $- 16 x + 12$ 
B)  $24 x + 12$ 
C)  $- 42 x ^ { 2 }$ 
D)  $- 16 x - 26$ 
A)  $- 16 x + 12$ 
B)  $24 x + 12$ 
C)  $- 42 x ^ { 2 }$ 
D)  $- 16 x - 26$

Question 13

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$\left( x ^ { 10 } + 11 \right) \left( x ^ { 10 } - 11 \right)$$

Accepted Answer

A)  $x ^ { 20 } + 22 x ^ { 10 } - 121$ 
B)  $x ^ { 100 } - 22 x ^ { 20 } - 121$ 
C)  $x ^ { 20 } - 121$ 
D)  $x ^ { 100 } - 22$ 
A)  $x ^ { 20 } + 22 x ^ { 10 } - 121$ 
B)  $x ^ { 100 } - 22 x ^ { 20 } - 121$ 
C)  $x ^ { 20 } - 121$ 
D)  $x ^ { 100 } - 22$

Question 14

Solve the problem.
-Write an expression for the area of the larger rectangle below in two different ways.

Accepted Answer

A)  $y ( 3 y + 8 ) ; 3 y ^ { 2 } + 8 y$ 
B)  $8 ( 3 y + y )$; $32 y$ 
C)  $3 y ( y + 8 )$; $3 y ^ { 2 } + 24 y$ 
D)  $2 y ( 6 y + 16 ) ; 12 y ^ { 2 } + 32 y$ 
A)  $y ( 3 y + 8 ) ; 3 y ^ { 2 } + 8 y$ 
B)  $8 ( 3 y + y )$; $32 y$ 
C)  $3 y ( y + 8 )$; $3 y ^ { 2 } + 24 y$ 
D)  $2 y ( 6 y + 16 ) ; 12 y ^ { 2 } + 32 y$

Question 15

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
-8

Accepted Answer

A)  Monomial, degree 0 
B)  Monomial, degree 1 
C)  Monomial, degree 8 
D)  Binomial, degree 0 
A)  Monomial, degree 0 
B)  Monomial, degree 1 
C)  Monomial, degree 8 
D)  Binomial, degree 0

Question 16

Use a vertical format to find the product.
-$$\begin{array} { r } 
5 z ^ { 3 } + 7 z ^ { 2 } + 4 z + 4 \
4 z + 7\
\hline 
\end{array}$$

Accepted Answer

A)  $20 z ^ { 4 } + 63 z ^ { 3 } + 65 z ^ { 2 } + 44 z + 28$ 
B)  $63 z ^ { 4 } + 77 z ^ { 3 } + 44 z ^ { 2 } + 44 z$ 
C)  $63 z ^ { 4 } + 63 z ^ { 3 } + 77 z ^ { 2 } + 28 z$ 
D)  $20 z ^ { 4 } + 35 z ^ { 3 } + 77 z ^ { 2 } + 44 z + 44$ 
A)  $20 z ^ { 4 } + 63 z ^ { 3 } + 65 z ^ { 2 } + 44 z + 28$ 
B)  $63 z ^ { 4 } + 77 z ^ { 3 } + 44 z ^ { 2 } + 44 z$ 
C)  $63 z ^ { 4 } + 63 z ^ { 3 } + 77 z ^ { 2 } + 28 z$ 
D)  $20 z ^ { 4 } + 35 z ^ { 3 } + 77 z ^ { 2 } + 44 z + 44$

Question 17

Multiply by using the rule for the square of a binomial.
-$$( x - 13 ) ^ { 2 }$$

Accepted Answer

A)  $x + 169$ 
B)  $x ^ { 2 } + 169$ 
C)  $169 x ^ { 2 } - 26 x + 169$ 
D)  $x ^ { 2 } - 26 x + 169$ 
A)  $x + 169$ 
B)  $x ^ { 2 } + 169$ 
C)  $169 x ^ { 2 } - 26 x + 169$ 
D)  $x ^ { 2 } - 26 x + 169$

Question 18

Use a vertical format to find the product.
-$$\begin{array} { r } 
x ^ { 3 } + 3 x - 2 \
x + 12 \
\hline
\end{array}$$

Accepted Answer

A)  $x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } + 34 x - 24$ 
B)  $x ^ { 3 } + 15 x ^ { 2 } + 34 x - 24$ 
C)  $x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } + 38 x + 24$ 
D)  $x ^ { 4 } + 3 x ^ { 2 } - 2 x + 12$ 
A)  $x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } + 34 x - 24$ 
B)  $x ^ { 3 } + 15 x ^ { 2 } + 34 x - 24$ 
C)  $x ^ { 4 } + 12 x ^ { 3 } + 3 x ^ { 2 } + 38 x + 24$ 
D)  $x ^ { 4 } + 3 x ^ { 2 } - 2 x + 12$

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

A)  $- 64 x$ 
B)  $- 12 x ^ { 3 }$ 
C)  $- 64 x ^ { 3 }$ 
D)  $- 12 \mathrm { x }$ 
A)  $- 64 x$ 
B)  $- 12 x ^ { 3 }$ 
C)  $- 64 x ^ { 3 }$ 
D)  $- 12 \mathrm { x }$

Solve the problem. -Find the area of a triangle with a base of 7x inches and a height of (10x + 4) inches.

Add the polynomials. - $\left( 9 x ^ { 3 } + 5 x + 7 \right) + \left( 8 x ^ { 2 } + 4 x + 5 \right)$

Multiply by using the rule for the square of a binomial. - $( 4 - 9 x ) ^ { 2 }$

Find the product. - $( 9 x - 1 ) \left( x ^ { 2 } - 5 x + 1 \right)$

Multiply the monomials. - $\left( - \frac { 1 } { 5 } x ^ { 7 } \right) \left( \frac { 1 } { 4 } x ^ { 9 } \right)$

Use a vertical format to add the polynomials. - -7 +7x-6 5 +8x-5

Use a vertical format to add the polynomials. - 9+3 3-5

Simplify the expression using the power rule. - $\left[ \left( - 7 ^ { 5 } \right) \right] ^ { 10 }$

Find the product. - $- 6 x ^ { 4 } \left( 8 x ^ { 5 } + 7 \right)$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $19 y ^ { 9 }$

Find the product. - $( x + 11 ) \left( x ^ { 3 } + 7 x - 8 \right)$

Subtract the polynomials. - $( 4 x - 7 ) - ( 20 x + 19 )$

Multiply using the rule for finding the product of the sum and difference of two terms. - $\left( x ^ { 10 } + 11 \right) \left( x ^ { 10 } - 11 \right)$

Solve the problem. -Write an expression for the area of the larger rectangle below in two different ways.

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. -8

Use a vertical format to find the product. - 5+7+4z+4 4z+7

Multiply by using the rule for the square of a binomial. - $( x - 13 ) ^ { 2 }$

Use a vertical format to find the product. - +3x-2 x+12

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

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

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

Solve the problem. -Find the area of a triangle with a base of 7x inches and a height of (10x + 4) inches.

Add the polynomials. - (9x3+5x+7)+(8x2+4x+5)\left( 9 x ^ { 3 } + 5 x + 7 \right) + \left( 8 x ^ { 2 } + 4 x + 5 \right)(9x3+5x+7)+(8x2+4x+5)

Multiply by using the rule for the square of a binomial. - (4−9x)2( 4 - 9 x ) ^ { 2 }(4−9x)2

Find the product. - (9x−1)(x2−5x+1)( 9 x - 1 ) \left( x ^ { 2 } - 5 x + 1 \right)(9x−1)(x2−5x+1)

Multiply the monomials. - (−15x7)(14x9)\left( - \frac { 1 } { 5 } x ^ { 7 } \right) \left( \frac { 1 } { 4 } x ^ { 9 } \right)(−51​x7)(41​x9)