Answers AZ-Common Core Algebra II ADivision of Polynomials

Division of Polynomials Answers

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The volume of a rectangular prism is (x3 – 3x2 + 5x – 3), and the area of its base is (x2 – 2). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism?

x minus 3 + StartFraction 7 x minus 9 Over x squared minus 2 EndFraction

x minus 3 + StartFraction 7 x minus 9 Over x cubed minus 3 x squared + 5 x minus 3 EndFraction

x minus 3 + StartFraction 7 x + 3 Over x squared minus 2 EndFraction

x minus 3 + StartFraction 7 x + 3 Over x cubed minus 3 x squared + 5 x minus 3 EndFraction

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Isla is dividing 3x3 + x2 – 12x – 4 by x + 2 using a division table. QuotientDivisor3x2– 5x– 2x3x3–5x2–2x+ 26x2ABWhat are the missing values in the table?

A = –10x; B = –4

A = –10x; B = 0

A = –3x; B = –4

A = –3x; B = 0

Tamara and Clyde got different answers when dividing 2x4 + 7x3 – 18x2 + 11x – 2 by 2x2 – 3x + 1. Analyze their individual work.Which statement about their answers is true?

Tamara’s work is correct because Clyde did not multiply the terms in the division table correctly.

Clyde’s work is correct because Tamara did not subtract the terms correctly.

Both students are correct.

Both students are incorrect.

Shelia is dividing x4 – 4x3 + 4x2 – 6x + 5 by x – 1 using a division table. QuotientDivisor x3– 3x2+ x– 5xx4–3x3x2A– 1–x33x2BCWhat are the missing values in the table?

A = –5x; B = 1x; C = 5

A = –5x; B = –1x; C = 5

A = 5x; B = –1x; C = 5

A = 5x; B = 1x; C = 5

Amal used the tabular method to show her work dividing –2x3 + 11x2 – 23x + 20 by x2 – 3x + 4. Amal’s Work: Quotient 2x+ 5 Divisorx2–2x35x26x2 + 5x2 = 11x2– 3x6x2–15x–8x + (–15x) = –23x + 4–8x20 Amal’s answer:Which statement about Amal’s work is true?

Amal’s work is correct.

Amal’s work is incorrect the wrong divisor is on the right side of the division table.

Amal’s work is incorrect because it includes a positive two instead of negative two in the answer.

Amal’s work is incorrect because the like terms in the division table do not simplify to the original polynomial.

The long division below shows the first term of the quotient. Which polynomial should be subtracted from the dividend first?

x + 3

x2 + x + 2

x3 + 2x2

x2 + 3x

What is the quotient of ?

x + 2

x - 2

x + 6

x - 6

What is the quotient of (x3 + 8) ÷ (x + 2)?

x2 + 2x + 4

x2 – 2x + 4

x2 + 4

x2 – 4

What is the first step of the following division problem?(8x3 – x2 + 6x + 7) ÷ (2x – 1)

Divide 8x3 by 2x.

Divide 2x by 8x3.

Divide 6x by 2x.

Divide 2x by 6x.

What is the quotient of the following division problem?

x + 2

x + 1

x2 + 3x + 2

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Division of Polynomials Answers

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