Use a vertical format to add the polynomials. -\[\begin{array} { r } 9 x ^ { 4 } + 2 x ^ { 3 } \\ 6 x ^ { 4 } + 7 x ^ { 3 } \\ \hline \end{array}\]

A) $15 x ^ { 4 } + 9 x ^ { 3 }$ B) $24 x ^ { 7 }$ C) $15 x ^ { 8 } + 9 x ^ { 6 }$ D) $24 \mathrm { x } ^ { 14 }$ A) $15 x ^ { 4 } + 9 x ^ { 3 }$ B) $24 x ^ { 7 }$ C) $15 x ^ { 8 } + 9 x ^ { 6 }$ D) $24 \mathrm { x } ^ { 14 }$

Use a vertical format to add the polynomials. -\[\begin{array} { l } 3 x ^ { 7 } + 6 x ^ { 6 } - 5 x \\ 2 x ^ { 7 } + 3 x ^ { 6 } - 4 x \\ \hline \end{array}\]

A) $5 x ^ { 7 } + 9 x ^ { 6 } - 9 x$ B) $5 \times ^ { 14 }$ C) $- 3 x ^ { 7 } + 6 x ^ { 6 } + 2 x$ D) $5 x + 9 x ^ { 7 } - 9 x ^ { 6 }$ A) $5 x ^ { 7 } + 9 x ^ { 6 } - 9 x$ B) $5 \times ^ { 14 }$ C) $- 3 x ^ { 7 } + 6 x ^ { 6 } + 2 x$ D) $5 x + 9 x ^ { 7 } - 9 x ^ { 6 }$

Use a vertical format to subtract the polynomials. -\[\begin{array} { l } 4 x ^ { 4 } - 4 x ^ { 3 } + 7 x ^ { 2 } \\ - \left( \quad - x ^ { 3 } - 9 x ^ { 2 } + x - 14 \right) \\ \hline \end{array}\]

A) $4 x ^ { 4 } - 3 x ^ { 3 } - 2 x ^ { 2 } + x - 14$ B) $4 x ^ { 4 } - 3 x ^ { 3 } + 16 x ^ { 2 } - x + 14$ C) $4 x ^ { 4 } - 5 x ^ { 3 } + 16 x ^ { 2 } + x - 14$ D) $4 x ^ { 4 } - 5 x ^ { 3 } - 2 x ^ { 2 } - x + 14$ A) $4 x ^ { 4 } - 3 x ^ { 3 } - 2 x ^ { 2 } + x - 14$ B) $4 x ^ { 4 } - 3 x ^ { 3 } + 16 x ^ { 2 } - x + 14$ C) $4 x ^ { 4 } - 5 x ^ { 3 } + 16 x ^ { 2 } + x - 14$ D) $4 x ^ { 4 } - 5 x ^ { 3 } - 2 x ^ { 2 } - x + 14$

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

A) $3 y ^ { 7 } - 18 y ^ { 6 } - 9$ B) $3 y ^ { 7 } - 6 y ^ { 6 } - 15$ C) $3 y ^ { 7 } - 18 y ^ { 6 } - 15$ D) $3 y ^ { 7 } - 6 y ^ { 6 } - 9$ A) $3 y ^ { 7 } - 18 y ^ { 6 } - 9$ B) $3 y ^ { 7 } - 6 y ^ { 6 } - 15$ C) $3 y ^ { 7 } - 18 y ^ { 6 } - 15$ D) $3 y ^ { 7 } - 6 y ^ { 6 } - 9$

Use a vertical format to add the polynomials. -\[\begin{array} { l } 5 x ^ { 8 } + 2 x ^ { 7 } - 8 x ^ { 6 } + 6 \\ 9 x ^ { 8 } + 2 x ^ { 7 } + 6 x ^ { 6 } - 9 \\ \hline \end{array}\]

A) $8 x ^ { 8 } + 8 x ^ { 7 } - 4 x ^ { 6 } + 11$ B) $16 x ^ { 42 } - 3$ C) $14 x ^ { 8 } + 4 x ^ { 7 } - 2 x ^ { 6 } - 3$ D) $14 x ^ { 16 } + 4 x ^ { 14 } - 2 x ^ { 12 } - 3$ A) $8 x ^ { 8 } + 8 x ^ { 7 } - 4 x ^ { 6 } + 11$ B) $16 x ^ { 42 } - 3$ C) $14 x ^ { 8 } + 4 x ^ { 7 } - 2 x ^ { 6 } - 3$ D) $14 x ^ { 16 } + 4 x ^ { 14 } - 2 x ^ { 12 } - 3$

Exam 5: Exponents and Polynomials

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

(Multiple Choice)

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Question 21

Use a vertical format to add the polynomials. - 9+2 6+7

(Multiple Choice)

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Question 22

Use a vertical format to add the polynomials. - 3+6-5x 2+3-4x

(Multiple Choice)

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Question 23

Find the product. - $( x + 9 ) ( x + 11 )$

(Multiple Choice)

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Question 24

Find the product. - $\left( \frac { 1 } { 4 } x - 9 \right) \left( \frac { 1 } { 3 } x + 8 \right)$

(Multiple Choice)

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Question 25

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( 6 x + 2 ) ( x + 9 )$

(Multiple Choice)

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Question 26

Use a vertical format to subtract the polynomials. - 4-4+7 - --9+x-14

(Multiple Choice)

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Question 27

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

(Multiple Choice)

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Question 28

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

(Multiple Choice)

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Question 29

Add the polynomials. - $\left( 7 y ^ { 5 } + 8 y ^ { 3 } \right) + \left( 6 y ^ { 5 } - 4 y ^ { 3 } \right)$

(Multiple Choice)

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Question 30

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $- 13 x ^ { 2 }$

(Multiple Choice)

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Question 31

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $13 y ^ { 3 } + 9 y ^ { 2 } + 3$

(Multiple Choice)

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Question 32

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $5 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 }$

(Multiple Choice)

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Question 33

Perform the indicated operations. - $\left[ \left( 3 x ^ { 9 } + 2 \right) - \left( - 12 x ^ { 7 } + 9 x ^ { 3 } \right) \right] - \left[ \left( 7 x ^ { 9 } - 7 x ^ { 5 } + 9 x \right) + \left( 11 x ^ { 3 } - 9 x - 10 \right) \right]$

(Multiple Choice)

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Question 34

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

(Multiple Choice)

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Question 35

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $- 16 y + 3$

(Multiple Choice)

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Question 36

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( 8 x - 11 ) ( 4 x - 5 )$

(Multiple Choice)

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Question 37

Multiply by using the rule for the square of a binomial. -The square painting in the figure measures x inches on each side. The painting is uniformly surrounded by a frame which measures 1 inch on each side. Write a polynomial in descending powers of x which expresses the Area of the square that includes the painting and the frame. Then write an expression for the area of the frame. (Hint: The area of the frame is the area of the painting and the frame minus the area of the painting.)

(Multiple Choice)

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Question 38

Use a vertical format to add the polynomials. - 5+2-8+6 9+2+6-9

(Multiple Choice)

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Question 39

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

(Multiple Choice)

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Question 40

Showing 21 - 40 of 122

Use a vertical format to add the polynomials. - 9+2 6+7

Use a vertical format to add the polynomials. - 3+6-5x 2+3-4x

Find the product. - $( x + 9 ) ( x + 11 )$

Find the product. - $\left( \frac { 1 } { 4 } x - 9 \right) \left( \frac { 1 } { 3 } x + 8 \right)$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( 6 x + 2 ) ( x + 9 )$

Use a vertical format to subtract the polynomials. - 4-4+7 - --9+x-14

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

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

Add the polynomials. - $\left( 7 y ^ { 5 } + 8 y ^ { 3 } \right) + \left( 6 y ^ { 5 } - 4 y ^ { 3 } \right)$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $- 13 x ^ { 2 }$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $13 y ^ { 3 } + 9 y ^ { 2 } + 3$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $5 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 }$

Perform the indicated operations. - $\left[ \left( 3 x ^ { 9 } + 2 \right) - \left( - 12 x ^ { 7 } + 9 x ^ { 3 } \right) \right] - \left[ \left( 7 x ^ { 9 } - 7 x ^ { 5 } + 9 x \right) + \left( 11 x ^ { 3 } - 9 x - 10 \right) \right]$

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

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $- 16 y + 3$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( 8 x - 11 ) ( 4 x - 5 )$

Use a vertical format to add the polynomials. - 5+2-8+6 9+2+6-9

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

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

Use a vertical format to add the polynomials. - 9+2 6+7

Use a vertical format to add the polynomials. - 3+6-5x 2+3-4x

Find the product. - (x+9)(x+11)( x + 9 ) ( x + 11 )(x+9)(x+11)

Find the product. - (14x−9)(13x+8)\left( \frac { 1 } { 4 } x - 9 \right) \left( \frac { 1 } { 3 } x + 8 \right)(41​x−9)(31​x+8)

Use the FOIL method to find the product. Express the product in descending powers of the variable. - (6x+2)(x+9)( 6 x + 2 ) ( x + 9 )(6x+2)(x+9)

Use a vertical format to subtract the polynomials. - 4-4+7 - --9+x-14

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

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

Add the polynomials. - (7y5+8y3)+(6y5−4y3)\left( 7 y ^ { 5 } + 8 y ^ { 3 } \right) + \left( 6 y ^ { 5 } - 4 y ^ { 3 } \right)(7y5+8y3)+(6y5−4y3)

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - −13x2- 13 x ^ { 2 }−13x2

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - 13y3+9y2+313 y ^ { 3 } + 9 y ^ { 2 } + 313y3+9y2+3

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - 5x4+3x3−7x25 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 }5x4+3x3−7x2

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

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - −16y+3- 16 y + 3−16y+3

Use the FOIL method to find the product. Express the product in descending powers of the variable. - (8x−11)(4x−5)( 8 x - 11 ) ( 4 x - 5 )(8x−11)(4x−5)

Use a vertical format to add the polynomials. - 5+2-8+6 9+2+6-9

Multiply the monomials. - (4x5)(−9x4)\left( 4 x ^ { 5 } \right) \left( - 9 x ^ { 4 } \right)(4x5)(−9x4)

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

Find the product. - $( x + 9 ) ( x + 11 )$

Find the product. - $\left( \frac { 1 } { 4 } x - 9 \right) \left( \frac { 1 } { 3 } x + 8 \right)$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( 6 x + 2 ) ( x + 9 )$

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

Add the polynomials. - $\left( 7 y ^ { 5 } + 8 y ^ { 3 } \right) + \left( 6 y ^ { 5 } - 4 y ^ { 3 } \right)$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $- 13 x ^ { 2 }$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $13 y ^ { 3 } + 9 y ^ { 2 } + 3$

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $5 x ^ { 4 } + 3 x ^ { 3 } - 7 x ^ { 2 }$

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

Identify the polynomial as a monomial, binomial, or trinomial. Give the degree of the polynomial. - $- 16 y + 3$

Use the FOIL method to find the product. Express the product in descending powers of the variable. - $( 8 x - 11 ) ( 4 x - 5 )$

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