Polynomials

Reviewed by Editorial Team

The ProProfs editorial team is comprised of experienced subject matter experts. They've collectively created over 10,000 quizzes and lessons, serving over 100 million users. Our team includes in-house content moderators and subject matter experts, as well as a global network of rigorously trained contributors. All adhere to our comprehensive editorial guidelines, ensuring the delivery of high-quality content.

Learn about Our Editorial Process

| By Tanmay Shankar

Tanmay Shankar

Community Contributor

Quizzes Created: 491 | Total Attempts: 1,846,919

| Attempts: 18,360

Questions

Feedback

During the Quiz End of Quiz

Difficulty

Easy First Hard First Sequential

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

1/15 Questions

Which of the following is not a polynomial:

Polynomials - Quiz

About This Quiz

Time: 30 Minute

2.

The degree of polynomial .
- 6
- 4
- 2
- 1
Correct Answer

A. 6
3.

Zero of the polynomial
- A = 0
- X = 0
- X = - 1
- X = 1
Correct Answer

A. X = 0

Explanation

The given polynomial has three zeros: x = 0, x = -1, and x = 1. However, the only zero mentioned in the options is x = 0. Therefore, the correct answer is x = 0.

Rate this question:

13
4.

If p(x) = 3x⁶ – 5x⁵ – x + 7, then p(2) equals:
- 36
- 37
- 73
- 63
Correct Answer

A. 37

Explanation

To find the value of p(2), we substitute 2 in place of x in the given polynomial expression p(x). So, p(2) = 3(2)^6 - 5(2)^5 - 2 + 7. Simplifying this expression, we get p(2) = 3(64) - 5(32) - 2 + 7 = 192 - 160 - 2 + 7 = 37. Therefore, the correct answer is 37.

Rate this question:

14
5.

The factorization of is:
Correct Answer

A.
6.

If x = 2 is a zero of the polynomial 2x² + 3x - p, then the value of p is:
- -4
- 0
- 8
- 14
Correct Answer

A. 14

Explanation

If x = 2 is a zero of the polynomial 2x^2 + 3x - p, it means that when x is substituted with 2 in the polynomial, the resulting expression will equal zero. To find the value of p, we can substitute x with 2 in the polynomial equation and set it equal to zero. By doing so, we get 2(2)^2 + 3(2) - p = 0. Simplifying this equation gives us 8 + 6 - p = 0. Combining like terms, we have 14 - p = 0. Solving for p, we find that p = 14.

Rate this question:

5
7.

If a + b = -1, then the value of a³ + b³ - 3ab is:
- 26
- 1
- -1
- -26
Correct Answer

A. -1

Explanation

The expression a3 + b3 - 3ab is a special case of the formula for the sum of cubes, which is (a + b)(a2 - ab + b2). In this case, since a + b = -1, we can substitute -1 for (a + b) in the formula. Simplifying further, we get (-1)(a2 - ab + b2). Since (-1)(-1) = 1, the expression simplifies to a2 - ab + b2. Plugging in the values of a and b, we get (-1)2 - (-1)(-1) + (-1)2, which simplifies to 1 + 1 + 1 = 3. Therefore, the correct answer is 1.

Rate this question:

4
8.

If x³ + 3x² + 3x + 1 is divided by (x + 1), then the remainder is
- 8
- -8
- 0
Correct Answer

A. 0

Explanation

When a polynomial is divided by (x + 1), we can use synthetic division to find the remainder. Plugging -1 into the polynomial, we get (-1)^3 + 3(-1)^2 + 3(-1) + 1 = -1 + 3 + (-3) + 1 = 0. Since the remainder is 0, this means that (x + 1) is a factor of the polynomial, and it divides evenly with no remainder.

Rate this question:

4
9.

The number of zeros of the polynomial x³ + x – 3 – 3x² is:
- Zero
- 1
- 2
- 3
Correct Answer

A. 3

Explanation

The given polynomial is a cubic polynomial, which means it is of degree 3. According to the Fundamental Theorem of Algebra, a polynomial of degree n has exactly n complex roots. Since the degree of the polynomial is 3, it will have 3 zeros. Therefore, the correct answer is 3.

Rate this question:

2
10.

If 2(a² + b²) = (a+b)², then
- A + b = 0
- A = b
- 2a = b
- Ab = 0
Correct Answer

A. A = b

Explanation

The given equation, 2(a^2 + b^2) = (a + b)^2, can be simplified as 2a^2 + 2b^2 = a^2 + 2ab + b^2. By rearranging the terms, we get a^2 - 2ab + b^2 = 0, which can be factored as (a - b)^2 = 0. Taking the square root of both sides, we get a - b = 0. Adding b to both sides, we find a = b. Therefore, the correct answer is a = b.

Rate this question:

2
11.

If (x + 2) and (x - 2) are factors of ax⁴ + 2x - 3x² + bx - 4, then the value of a + b is:
- 1
- -1
- 3
- -3
Correct Answer

A. -1

Explanation

If (x + 2) and (x - 2) are factors of the given expression, it means that when we substitute x = -2 and x = 2 into the expression, the result is equal to zero. By substituting these values, we can determine the values of a and b. When x = -2, the expression becomes 16a - 4 + 12 - 2b - 4 = 0. Simplifying this equation gives us 16a - 2b + 4 = 0. Similarly, when x = 2, the expression becomes 16a + 4 + 12 + 2b - 4 = 0, which simplifies to 16a + 2b + 16 = 0. Solving these two equations simultaneously, we find that a = -1 and b = 0. Therefore, the value of a + b is -1 + 0 = -1.

Rate this question:

2
12.

If , then the value of (x² - 4x + 1) is:
- 3
- Zero
- 1
- -1
Correct Answer

A. Zero

Explanation

The given expression is a quadratic equation in the form of ax^2 + bx + c. In this case, a = 1, b = -4, and c = 1. To find the value of the expression, we can substitute the given value of x and evaluate the expression. When x = 2, the expression becomes (2^2 - 4*2 + 1) = 4 - 8 + 1 = -3 + 1 = -2. Therefore, the value of (x^2 - 4x + 1) is not equal to 3, 1, or -1, but it is equal to zero.

Rate this question:

2
13.

The remainder on factorization of polynomial x³ + x – 3 – 3x² by x - 2 is:
- Zero
- 2
- 3
- 1
Correct Answer

A. 3

Explanation

When we divide the polynomial x^3 + x - 3 - 3x^2 by x - 2 using long division, we find that the remainder is 3. This means that the polynomial cannot be completely divided by x - 2, and there is a remainder of 3 left over. Therefore, the correct answer is 3.

Rate this question:

1
14.

Find the zeros of the polynomial x² - 3:
Correct Answer

A.

Explanation

The zeros of a polynomial are the values of x for which the polynomial equals zero. In this case, the polynomial is x^2 - 3. To find the zeros, we set the polynomial equal to zero and solve for x. So, x^2 - 3 = 0. Adding 3 to both sides gives x^2 = 3. Taking the square root of both sides gives x = ±√3. Therefore, the zeros of the polynomial x^2 - 3 are ±√3.

Rate this question:

5
15.

Consider the polynomial P(x) = 3x^4 - 4x^3 + 2x^2 - x + 7. What is the remainder when P(x) is divided by (x - 1)?
- 5
- 7
- 8
- 10
Correct Answer

A. 7

Explanation

To find the remainder of the polynomial P(x) when divided by (x - 1), we can use the Remainder Theorem. According to this theorem, the remainder of the division of a polynomial P(x) by a linear divisor (x - a) is P(a). In this case, we need to evaluate P(1):
P(1) = 3(1)^4 - 4(1)^3 + 2(1)^2 - 1 + 7
= 31 - 41 + 2*1 - 1 + 7
= 3 - 4 + 2 - 1 + 7
= 7

Rate this question:

14