Question 1

Use the FOIL method to find the product. Express the product in descending powers of the variable.
-$$( x + 10 ) ( 7 x - 10 )$$

Accepted Answer

A)  $7 x ^ { 2 } + 60 x - 100$ 
B)  $7 x ^ { 2 } + 58 x - 100$ 
C)  $7 x ^ { 2 } - 100 x + 60$ 
D)  $7 x ^ { 2 } + 60 x + 60$ 
A)  $7 x ^ { 2 } + 60 x - 100$ 
B)  $7 x ^ { 2 } + 58 x - 100$ 
C)  $7 x ^ { 2 } - 100 x + 60$ 
D)  $7 x ^ { 2 } + 60 x + 60$

Question 2

Multiply the monomials.
-$$\left( \frac { 1 } { 4 } x ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } \right)$$

Accepted Answer

A)  $- \frac { 1 } { 20 } x ^ { 16 }$ 
B)  $- \frac { 1 } { 20 } x ^ { 10 }$ 
C)  $\frac { 1 } { 20 } x ^ { 10 }$ 
D)  $\frac { 1 } { 20 } x ^ { 16 }$ 
A)  $- \frac { 1 } { 20 } x ^ { 16 }$ 
B)  $- \frac { 1 } { 20 } x ^ { 10 }$ 
C)  $\frac { 1 } { 20 } x ^ { 10 }$ 
D)  $\frac { 1 } { 20 } x ^ { 16 }$

Question 3

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
--14x

Accepted Answer

A)  Monomial, degree 1 
B)  Monomial, degree 0 
C)  Monomial, degree -14 
D)  Binomial, degree 0 
A)  Monomial, degree 1 
B)  Monomial, degree 0 
C)  Monomial, degree -14 
D)  Binomial, degree 0

Question 4

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$( 7 - 5 r ) ( 7 + 5 r )$$

Accepted Answer

A)  $49 - 5 r ^ { 2 }$ 
B)  $49 - 25 r ^ { 2 }$ 
C)  $49 + 70 r - 25 r ^ { 2 }$ 
D)  $49 - 70 r - 25 r ^ { 2 }$ 
A)  $49 - 5 r ^ { 2 }$ 
B)  $49 - 25 r ^ { 2 }$ 
C)  $49 + 70 r - 25 r ^ { 2 }$ 
D)  $49 - 70 r - 25 r ^ { 2 }$

Question 5

Simplify the expression using the power rule.
-$\left( y ^ { 2 } \right) ^ { 8 }$

Accepted Answer

A)  $\mathrm { y } ^ { 10 }$ 
B)  $8 \mathrm { y } ^ { 16 }$ 
C)  $\mathrm { y } ^ { 16 }$ 
D)  $8 \mathrm { y } ^ { 2 }$ 
A)  $\mathrm { y } ^ { 10 }$ 
B)  $8 \mathrm { y } ^ { 16 }$ 
C)  $\mathrm { y } ^ { 16 }$ 
D)  $8 \mathrm { y } ^ { 2 }$

Question 6

Add the polynomials.
-$$\left( 2 y ^ { 7 } - 2 y ^ { 5 } - 2 y \right) + \left( 7 y ^ { 7 } - 7 y ^ { 5 } + 5 y \right)$$

Accepted Answer

A)  $5 y ^ { 7 } - 5 y ^ { 5 } + 3 y$ 
B)  $3 y 13$ 
C)  $9 y - 9 y ^ { 7 } + 3 y ^ { 5 }$ 
D)  $9 y ^ { 7 } - 9 y ^ { 5 } + 3 y$ 
A)  $5 y ^ { 7 } - 5 y ^ { 5 } + 3 y$ 
B)  $3 y 13$ 
C)  $9 y - 9 y ^ { 7 } + 3 y ^ { 5 }$ 
D)  $9 y ^ { 7 } - 9 y ^ { 5 } + 3 y$

Question 7

Multiply by using the rule for the square of a binomial.
-$$( 6 x - 5 ) ^ { 2 }$$

Accepted Answer

A)  $6 x ^ { 2 } - 60 x + 25$ 
B)  $36 x ^ { 2 } + 25$ 
C)  $6 x ^ { 2 } + 25$ 
D)  $36 x ^ { 2 } - 60 x + 25$ 
A)  $6 x ^ { 2 } - 60 x + 25$ 
B)  $36 x ^ { 2 } + 25$ 
C)  $6 x ^ { 2 } + 25$ 
D)  $36 x ^ { 2 } - 60 x + 25$

Question 8

Multiply the monomials.
-$\left( 6 x ^ { 7 } \right) \left( 4 x ^ { 2 } \right)$

Accepted Answer

A)  $24 x ^ { 14 }$ 
B)  $- 24 x ^ { 14 }$ 
C)  $- 24 x ^ { 9 }$ 
D)  $24 x ^ { 9 }$ 
A)  $24 x ^ { 14 }$ 
B)  $- 24 x ^ { 14 }$ 
C)  $- 24 x ^ { 9 }$ 
D)  $24 x ^ { 9 }$

Question 9

Find the product.
-$$( 2 x - 10 ) ( x + 9 )$$

Accepted Answer

A)  $x ^ { 2 } - 90 x + 8$ 
B)  $2 x ^ { 2 } + 7 x - 90$ 
C)  $x ^ { 2 } + 8 x + 7$ 
D)  $2 x ^ { 2 } + 8 x - 90$ 
A)  $x ^ { 2 } - 90 x + 8$ 
B)  $2 x ^ { 2 } + 7 x - 90$ 
C)  $x ^ { 2 } + 8 x + 7$ 
D)  $2 x ^ { 2 } + 8 x - 90$

Question 10

Subtract the polynomials.
-$$\left( 7 x ^ { 2 } + 3 x ^ { 4 } - 6 - 2 x ^ { 3 } \right) - \left( - 8 + 8 x ^ { 3 } + 8 x ^ { 4 } + 3 x ^ { 2 } \right)$$

Accepted Answer

A)  $- 5 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } - 14$ 
B)  $11 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } + 2$ 
C)  $- 5 x ^ { 4 } - 10 x ^ { 3 } + 4 x ^ { 2 } + 2$ 
D)  $11 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } - 14$ 
A)  $- 5 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } - 14$ 
B)  $11 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } + 2$ 
C)  $- 5 x ^ { 4 } - 10 x ^ { 3 } + 4 x ^ { 2 } + 2$ 
D)  $11 x ^ { 4 } + 6 x ^ { 3 } + 10 x ^ { 2 } - 14$

Question 11

Multiply using the rule for finding the product of the sum and difference of two terms.
-$$( 8 x + 13 ) ( 8 x - 13 )$$

Accepted Answer

A)  $x ^ { 2 } - 169$ 
B)  $64 x ^ { 2 } - 208 x - 169$ 
C)  $64 x ^ { 2 } + 208 x - 169$ 
D)  $64 \mathrm { x } ^ { 2 } - 169$ 
A)  $x ^ { 2 } - 169$ 
B)  $64 x ^ { 2 } - 208 x - 169$ 
C)  $64 x ^ { 2 } + 208 x - 169$ 
D)  $64 \mathrm { x } ^ { 2 } - 169$

Question 12

Find the product.
-$$\left( x ^ { 2 } - 3 x + 1 \right) ( 5 x )$$

Accepted Answer

A)  $5 x ^ { 3 } - 15 x ^ { 2 } + 5 x$ 
B)  $5 x ^ { 3 } - 14 x ^ { 2 } + 2 x$ 
C)  $5 x ^ { 3 } - 15 x ^ { 2 } - 8 x$ 
D)  $5 x ^ { 3 } + 16 x ^ { 2 } + 5 x$ 
A)  $5 x ^ { 3 } - 15 x ^ { 2 } + 5 x$ 
B)  $5 x ^ { 3 } - 14 x ^ { 2 } + 2 x$ 
C)  $5 x ^ { 3 } - 15 x ^ { 2 } - 8 x$ 
D)  $5 x ^ { 3 } + 16 x ^ { 2 } + 5 x$

Question 13

Multiply the monomials.
-$$\left( - 6 x ^ { 5 } \right) \left( 5 x ^ { 3 } \right)$$

Accepted Answer

A)  $- 30 x ^ { 15 }$ 
B)  $30 x ^ { 15 }$ 
C)  $30 x ^ { 8 }$ 
D)  $- 30 x ^ { 8 }$ 
A)  $- 30 x ^ { 15 }$ 
B)  $30 x ^ { 15 }$ 
C)  $30 x ^ { 8 }$ 
D)  $- 30 x ^ { 8 }$

Question 14

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
-$$17 x ^ { 6 } + 7 x - 1$$

Accepted Answer

A)  Trinomial, degree 6 
B)  Binomial, degree 7 
C)  Trinomial, degree 7 
D)  Trinomial, degree 8 
A)  Trinomial, degree 6 
B)  Binomial, degree 7 
C)  Trinomial, degree 7 
D)  Trinomial, degree 8

Question 15

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

Accepted Answer

A)  $x ^ { 4 } + 2 x ^ { 3 } - 12 x ^ { 2 } - 26 x - 35$ 
B)  $- 7 x ^ { 4 } - 2 x ^ { 3 } - 9 x ^ { 2 } - 16 x - 35$ 
C)  $- 7 x ^ { 4 } - 21 x ^ { 3 } + 35 x ^ { 2 }$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 } - 16 x + 35$ 
A)  $x ^ { 4 } + 2 x ^ { 3 } - 12 x ^ { 2 } - 26 x - 35$ 
B)  $- 7 x ^ { 4 } - 2 x ^ { 3 } - 9 x ^ { 2 } - 16 x - 35$ 
C)  $- 7 x ^ { 4 } - 21 x ^ { 3 } + 35 x ^ { 2 }$ 
D)  $x ^ { 4 } + 2 x ^ { 3 } - 15 x ^ { 2 } - 16 x + 35$

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

A)  $4 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 10$ 
B)  $6 x ^ { 5 } + 14 x ^ { 2 } + 6 x + 7$ 
C)  $6 x ^ { 5 } + 18 x ^ { 3 } + 30 x$ 
D)  $4 x ^ { 3 } + 14 x ^ { 2 } + 26 x + 10$ 
A)  $4 x ^ { 3 } + 2 x ^ { 2 } + 6 x + 10$ 
B)  $6 x ^ { 5 } + 14 x ^ { 2 } + 6 x + 7$ 
C)  $6 x ^ { 5 } + 18 x ^ { 3 } + 30 x$ 
D)  $4 x ^ { 3 } + 14 x ^ { 2 } + 26 x + 10$

Question 18

Find the product.
-$$x ( x - 5 )$$

Accepted Answer

A)  $- 4 x ^ { 2 }$ 
B)  $2 x - 5$ 
C)  $x ^ { 2 } - 5$ 
D)  $x ^ { 2 } - 5 x$ 
A)  $- 4 x ^ { 2 }$ 
B)  $2 x - 5$ 
C)  $x ^ { 2 } - 5$ 
D)  $x ^ { 2 } - 5 x$

Question 19

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 man with 10 years of education as a
Point on the appropriate graph. $$\begin{array} { l } 
\mathrm { M } = 224 \mathrm { x } ^ { 2 } - 1266 \mathrm { x } + 20,106 \
\mathrm {~W} = 287 \mathrm { x } ^ { 2 } - 4030 \mathrm { x } + 33,761
\end{array}$$

Accepted Answer

A)  (10, 41,240) 
B)  (10, 58,431) 
C)  (10, 29,846) 
D)  (10, 22,161) 
A)  (10, 41,240) 
B)  (10, 58,431) 
C)  (10, 29,846) 
D)  (10, 22,161)

Question 20

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial.
-$$- 8 y ^ { 6 } + 3$$

Accepted Answer

A)  Monomial, degree -8 
B)  Binomial, degree 0 
C)  Binomial, degree 7 
D)  Binomial, degree 6 
A)  Monomial, degree -8 
B)  Binomial, degree 0 
C)  Binomial, degree 7 
D)  Binomial, degree 6

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( x + 10 ) ( 7 x - 10 )$

Multiply the monomials. - $\left( \frac { 1 } { 4 } x ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } \right)$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. --14x

Multiply using the rule for finding the product of the sum and difference of two terms. - $( 7 - 5 r ) ( 7 + 5 r )$

Simplify the expression using the power rule. - $\left( y ^ { 2 } \right) ^ { 8 }$

Add the polynomials. - $\left( 2 y ^ { 7 } - 2 y ^ { 5 } - 2 y \right) + \left( 7 y ^ { 7 } - 7 y ^ { 5 } + 5 y \right)$

Multiply by using the rule for the square of a binomial. - $( 6 x - 5 ) ^ { 2 }$

Multiply the monomials. - $\left( 6 x ^ { 7 } \right) \left( 4 x ^ { 2 } \right)$

Find the product. - $( 2 x - 10 ) ( x + 9 )$

Subtract the polynomials. - $\left( 7 x ^ { 2 } + 3 x ^ { 4 } - 6 - 2 x ^ { 3 } \right) - \left( - 8 + 8 x ^ { 3 } + 8 x ^ { 4 } + 3 x ^ { 2 } \right)$

Multiply using the rule for finding the product of the sum and difference of two terms. - $( 8 x + 13 ) ( 8 x - 13 )$

Find the product. - $\left( x ^ { 2 } - 3 x + 1 \right) ( 5 x )$

Multiply the monomials. - $\left( - 6 x ^ { 5 } \right) \left( 5 x ^ { 3 } \right)$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $17 x ^ { 6 } + 7 x - 1$

Use a vertical format to find the product. - +3x-5 -x-7

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

Use a vertical format to find the product. - +3x+5 4x+2

Find the product. - $x ( x - 5 )$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $- 8 y ^ { 6 } + 3$

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

Use the FOIL method to find the product. Express the product in descending powers of the variable. - (x+10)(7x−10)( x + 10 ) ( 7 x - 10 )(x+10)(7x−10)

Multiply the monomials. - (14x8)(15x2)\left( \frac { 1 } { 4 } x ^ { 8 } \right) \left( \frac { 1 } { 5 } x ^ { 2 } \right)(41​x8)(51​x2)

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. --14x

Multiply using the rule for finding the product of the sum and difference of two terms. - (7−5r)(7+5r)( 7 - 5 r ) ( 7 + 5 r )(7−5r)(7+5r)

Simplify the expression using the power rule. - (y2)8\left( y ^ { 2 } \right) ^ { 8 }(y2)8

Add the polynomials. - (2y7−2y5−2y)+(7y7−7y5+5y)\left( 2 y ^ { 7 } - 2 y ^ { 5 } - 2 y \right) + \left( 7 y ^ { 7 } - 7 y ^ { 5 } + 5 y \right)(2y7−2y5−2y)+(7y7−7y5+5y)

Multiply by using the rule for the square of a binomial. - (6x−5)2( 6 x - 5 ) ^ { 2 }(6x−5)2

Multiply the monomials. - (6x7)(4x2)\left( 6 x ^ { 7 } \right) \left( 4 x ^ { 2 } \right)(6x7)(4x2)

Find the product. - (2x−10)(x+9)( 2 x - 10 ) ( x + 9 )(2x−10)(x+9)

Subtract the polynomials. - (7x2+3x4−6−2x3)−(−8+8x3+8x4+3x2)\left( 7 x ^ { 2 } + 3 x ^ { 4 } - 6 - 2 x ^ { 3 } \right) - \left( - 8 + 8 x ^ { 3 } + 8 x ^ { 4 } + 3 x ^ { 2 } \right)(7x2+3x4−6−2x3)−(−8+8x3+8x4+3x2)

Multiply using the rule for finding the product of the sum and difference of two terms. - (8x+13)(8x−13)( 8 x + 13 ) ( 8 x - 13 )(8x+13)(8x−13)

Find the product. - (x2−3x+1)(5x)\left( x ^ { 2 } - 3 x + 1 \right) ( 5 x )(x2−3x+1)(5x)

Multiply the monomials. - (−6x5)(5x3)\left( - 6 x ^ { 5 } \right) \left( 5 x ^ { 3 } \right)(−6x5)(5x3)

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - 17x6+7x−117 x ^ { 6 } + 7 x - 117x6+7x−1