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?

A
x minus 3 + StartFraction 7 x minus 9 Over x squared minus 2 EndFraction
Option A
B
x minus 3 + StartFraction 7 x minus 9 Over x cubed minus 3 x squared + 5 x minus 3 EndFraction
Option B
C
x minus 3 + StartFraction 7 x + 3 Over x squared minus 2 EndFraction
Option C
D
x minus 3 + StartFraction 7 x + 3 Over x cubed minus 3 x squared + 5 x minus 3 EndFraction
Option D
2
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What is the quotient of (x3 + 3x2 + 5x + 3) ÷ (x + 1)?

A
x2 + 4x + 9
B
x2 + 2x
C
x2 + 2x + 3
D
x2 + 3x + 8
3

If (x2 – 4) ÷ (x + 2) = x – 2, which polynomial should fill in the blank below?(x + 2) ´ ______ = x2 – 4

A
x2 – 4
B
x – 2
C
x + 2
D
x2 – 2
4

What is the quotient of ?

Question illustration
A
x + 2
B
x - 2
C
x + 6
D
x - 6
5

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

A
x + 2
B
x – 2
C
x + 10
D
x + 6
6

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
A = –10x; B = –4
B
A = –10x; B = 0
C
A = –3x; B = –4
D
A = –3x; B = 0
7

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
8

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
9

What is the quotient of ?

Question illustration
A
x + 2
B
x – 2
C
x – 8
D
x + 8
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
11

The quotient of (x4 + 5x3 – 3x – 15) and (x3 – 3) is a polynomial. What is the quotient?

A
x7 + 5x6 – 6x4 – 30x3 + 9x + 45
B
x – 5
C
x + 5
D
x7 + 5x6 + 6x4 + 30x3 + 9x + 45
12

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

A
x2 + 2x + 4
B
x2 – 2x + 4
C
x2 + 4
D
x2 – 4
13

What is the remainder of the following division problem?

Question illustration
A
x
B
1
C
0
D
–1
14

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.
15

What is the first term of the quotient of the following division problem?(x3 – 1) ÷ (x + 2)

A
–0.5
B
1
C
x2
D
x4

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