AnswersAZ-Common Core Algebra II ASum and Difference of Two Cubes

Division of Polynomials Answers

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1
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What is the quotient of (3x4 – 4x2 + 8x – 1) ÷ (x – 2)?

A
3x3 + 6x2 + 8x + 24 –
Option A
B
3x3 + 6x2 + 8x + 24 +
Option B
C
3x3 + 6x2 + 8x + 24 +
Option C
D
3x3 + 6x2 + 8x + 24 –
Option D
2
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What is the quotient of ?

Question illustration
A
x + 2
B
x - 2
C
x + 6
D
x - 6
3

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?

Question illustration
A
Amal’s work is correct.
B
Amal’s work is incorrect the wrong divisor is on the right side of the division table.
C
Amal’s work is incorrect because it includes a positive two instead of negative two in the answer.
D
Amal’s work is incorrect because the like terms in the division table do not simplify to the original polynomial.
4

The quotient of (x5 – 3x3 – 3x2 – 10x + 15) and (x2 – 5) is a polynomial. What is the quotient?

A
x5 – 3x3 – 2x2 – 10x + 10
B
x7 – 8x5 – 3x4 + 5x3 + 30x2 + 50x – 75
C
x3 + 2x – 3
D
x5 – 3x3 – 4x2 – 10x + 20
5

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
A = –5x; B = 1x; C = 5
B
A = –5x; B = –1x; C = 5
C
A = 5x; B = –1x; C = 5
D
A = 5x; B = 1x; C = 5
6

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

A
x2 + 2x + 4
B
x2 – 2x + 4
C
x2 + 4
D
x2 – 4
7

What is the remainder of the following division problem?

Question illustration
A
x
B
1
C
0
D
–1
8

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?

Question illustration
A
Tamara’s work is correct because Clyde did not multiply the terms in the division table correctly.
B
Clyde’s work is correct because Tamara did not subtract the terms correctly.
C
Both students are correct.
D
Both students are incorrect.
9

What is the quotient of (x3 + 6x2 + 11x + 6) ÷ (x2 + 4x + 3)?

A
x + 2
B
x – 2
C
x + 10
D
x + 6
10

The area of a rectangle is (x4 + 4x3 + 3x2 – 4x – 4), and the length of the rectangle is (x3 + 5x2 + 8x + 4). If area = length × width, what is the width of the rectangle?

A
x + 1
B
x – 9
C
x + 4
D
x – 1

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