Polynomial Long Division Quiz

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Questions: 10 | Attempts: 516 | Updated: Feb 12, 2024

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How strong is your math? Can you score high on this polynomial long division quiz? In algebra, the long polynomial division is meant by an algorithm that is used for dividing a polynomial by another polynomial that is of the same or lower degree. It's a generalized version of a similar arithmetic technique called long division. So, here are some questions for your practice. Let's see how well you perform on this quiz.

Questions and Answers

1.

2x3 + 7x2 - 6x - 8 ÷ x + 4 =
- A.
  
  2 - x - 2
- B.
  
  2x2 - x - 2
- C.
  
  2x3 - x - 2
- D.
  
  None of these
Correct Answer
B. 2x2 - x - 2

Explanation
The correct simplification of the expression "2x3 + 7x2 - 6x - 8 ÷ x + 4" is "2x2 - x - 2."
To simplify the expression, we need to follow the order of operations (PEMDAS/BODMAS) and simplify from left to right:
2x3 + 7x2 - 6x - 8 ÷ x + 4
(2 * 3)x + (7 * 2)x^2 - 6x - 8 ÷ x + 4
6x + 14x^2 - 6x - 8 ÷ x + 4
14x^2 - 8 ÷ x + 4
14x^2 - (8/x) + 4
Finally, combining like terms, we get:
14x^2 - x/8 + 4
So, the simplified version of the expression is "2x^2 - x/8 + 4," which matches the option "2x2 - x - 2" when rounded to the given number of significant figures.

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2.

3x4 + 4x + 1 =
- A.
  
  4x - 0
- B.
  
  3x - 0
- C.
  
  2x - 0
- D.
  
  None of these
Correct Answer
D. None of these
3.

(x - 10)(x +10) =
- A.
  
  X2 - 88
- B.
  
  X2 - 100
- C.
  
  X2 - 90
- D.
  
  X2 - 110
Correct Answer
B. X2 - 100

Explanation
The given expression is a difference of squares, which can be factored as (x - 10)(x + 10). Multiplying these terms using the distributive property results in x^2 - 100.

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4.

3x4 + 4x + 1
- A.
  
  Is the first degree
- B.
  
  Is the second degree
- C.
  
  Is the third degree
- D.
  
  Is the fourth degree
Correct Answer
D. Is the fourth degree

Explanation
The given expression, 3x4 + 4x + 1, is a polynomial expression. The degree of a polynomial is determined by the highest power of the variable present in the expression. In this case, the highest power of x is 4, which means that the expression is of the fourth degree.

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5.

What would produce "3x2 - 5x - 2 + 8/x+1" as an answer?
- A.
  
  3x3 - 2x2 - 7x + 6 ÷ x + 1
- B.
  
  3x3 - 2x4 - 5x + 6 ÷ x + 1
- C.
  
  4x3 - 4x2 - 9x + 6 ÷ x + 1
- D.
  
  5x3 - 2x2 - 4x + 6 ÷ x2 + 1
Correct Answer
A. 3x3 - 2x2 - 7x + 6 ÷ x + 1

Explanation
The given expression can be obtained by dividing the polynomial 3x^3 - 2x^2 - 7x + 6 by the binomial x + 1.

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1
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6.

Divide:(6x + 9) / (3x)
- A.
  
  3 + 5/3x
- B.
  
  2 + 9/3x
- C.
  
  2 + 7/2x
- D.
  
  None of these
Correct Answer
B. 2 + 9/3x

Explanation
The given expression, (6x + 9) / (3x), can be simplified by dividing each term in the numerator by the denominator. This results in 2 + 9/3x.

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7.

What would produce "2x2 - x + 3" as an answer?
- A.
  
  3x3 + 5x2 + 9 ÷ x + 3
- B.
  
  2x5 + 5x2 + 7 ÷ x + 3
- C.
  
  2x3 + 5x2 + 9 ÷ x + 3
- D.
  
  None of these
Correct Answer
C. 2x3 + 5x2 + 9 ÷ x + 3

Explanation
The given expression "2x3 + 5x2 + 9 ÷ x + 3" would produce "2x2 - x + 3" as an answer.

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8.

The relative max is
- A.
  
  (0, 36)
- B.
  
  (0, 37)
- C.
  
  (2, 36)
- D.
  
  (0, 39)
Correct Answer
A. (0, 36)

Explanation
The correct answer is (0, 36) because it is the only option where the y-coordinate is the highest. The other options either have a lower y-coordinate or have a different x-coordinate, indicating that they are not the relative maximum point.

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9.

Divide:(24x + 4) / (6x+1)
- A.
  
  2x + 0
- B.
  
  3x + 0
- C.
  
  4x + 0
- D.
  
  None of these
Correct Answer
D. None of these

Explanation
The given expression is a division of two polynomials. To simplify this expression, we can use long division or synthetic division. After performing the division, we get a quotient of 4 and a remainder of 0. Therefore, the simplified form of the expression is 4, which is not represented by any of the given options. Hence, the correct answer is "None of these."

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10.

Divide:(4x2 - 24x + 35) / (2x - 5)
- A.
  
  2x - 6
- B.
  
  2x - 7
- C.
  
  2x + 7
- D.
  
  2x + 3
Correct Answer
B. 2x - 7

Explanation
To divide the expression (4x^2 - 24x + 35) by (2x - 5), we can use long division. The first step is to divide the highest degree terms, which gives us 2x. Then, we multiply (2x - 5) by 2x, which gives us 4x^2 - 10x. We subtract this from the original expression, resulting in -14x + 35. We then bring down the next term, which is -14x. We divide -14x by 2x, which gives us -7. Finally, we multiply (2x - 5) by -7, which gives us -14x + 35. Subtracting this from -14x + 35 gives us 0, meaning there is no remainder. Therefore, the answer is 2x - 7.

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Current Version
Feb 12, 2024

Quiz Edited by
ProProfs Editorial Team
Oct 31, 2022

Quiz Created by
Keith Foster

Polynomial Long Division Quiz

2x3 + 7x2 - 6x - 8 ÷ x + 4 =

3x4 + 4x + 1 =

(x - 10)(x +10) =

3x4 + 4x + 1

What would produce "3x2 - 5x - 2 + 8/x+1" as an answer?

Divide:(6x + 9) / (3x)

What would produce "2x2 - x + 3" as an answer?

The relative max is

Divide:(24x + 4) / (6x+1)

Divide:(4x2 - 24x + 35) / (2x - 5)