Polynomial Long Division Quiz

Created by ProProfs Editorial Team

The editorial team at ProProfs Quizzes consists of a select group of subject experts, trivia writers, and quiz masters who have authored over 10,000 quizzes taken by more than 100 million users. This team includes our in-house seasoned quiz moderators and subject matter experts. Our editorial experts, spread across the world, are rigorously trained using our comprehensive guidelines to ensure that you receive the highest quality quizzes.

Learn about Our Editorial Process

| By Keith Foster

Keith Foster, Quiz Creator

Keith is a dedicated member of ProProfs.com, specializing in creating engaging and diverse quizzes. His passion for knowledge and creativity drives him to develop captivating and enjoyable content. Keith's commitment to high-quality standards and innovative ideas ensures his quizzes are informative and entertaining for a wide audience.

Quizzes Created: 1110 | Total Attempts: 2,473,266

Questions: 10 | Attempts: 544 | Updated: Feb 12, 2024

Questions

Settings

Feedback

During the Quiz End of Quiz

Difficulty

Sequential Easy First Hard First

Play as

Quiz Flashcard

Create your own Quiz

Share on Facebook Share on Twitter Share on Whatsapp Share on Pinterest Share on Email Copy to Clipboard Embed on your website

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.

Rate this question:

0
0
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.

Rate this question:
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.

Rate this question:
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.

Rate this question:

1
0
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.

Rate this question:
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.

Rate this question:
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.

Rate this question:
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."

Rate this question:
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.

Rate this question:

Quiz Review Timeline +

Our quizzes are rigorously reviewed, monitored and continuously updated by our expert board to maintain accuracy, relevance, and timeliness.

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)