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Polynomials Practice Questions

Class 10 · Mathematics · 1551 free MCQs with instant results and detailed explanations.

1551
Total
581
Easy
693
Medium
277
Hard

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Topics in Polynomials

Division Algorithm 485
Relationship between Zeros and Coefficients 433
Zeros of a Polynomial 633

Sample Questions from Polynomials

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the degree of the polynomial 3x^4 + 2x^3 - x + 7?
A. 4
B. 3
C. 2
D. 1
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is the highest power of the variable present in it. Here, the highest power is 4.
Q2
Easy
Which of the following is a zero of the polynomial p(x) = x^2 + 4x + 4?
A. -2
B. 2
C. 0
D. 4
Show Answer & Explanation
Correct Answer: A
The polynomial can be factored as (x + 2)(x + 2), indicating that x = -2 is a repeated zero.
Q3
Easy
The polynomial q(x) = 2x^3 - 3x^2 + x - 5 has how many zeros?
A. 1
B. 2
C. 3
D. None
Show Answer & Explanation
Correct Answer: C
A cubic polynomial always has 3 zeros, counting multiplicity, according to the Fundamental Theorem of Algebra.
Q4
Medium
Which of the following is a property of the zeros of the polynomial f(x) = x^3 - 6x^2 + 11x - 6?
A. There are three distinct real zeros.
B. The zeros are all negative.
C. The zeros include complex numbers.
D. There is one zero and two imaginary zeros.
Show Answer & Explanation
Correct Answer: A
Using the Rational Root Theorem or synthetic division, we find that the polynomial has three distinct real zeros.
Q5
Medium
If the polynomial Q(x) = x^2 + bx + c has zeros that are equal, which of the following must be true?
A. b^2 - 4c = 0
B. b^2 + 4c = 0
C. b + c = 0
D. b^2 = 4c
Show Answer & Explanation
Correct Answer: A
For a quadratic to have equal zeros, the discriminant must be zero. Hence, b² - 4c = 0.
Q6
Medium
For the polynomial P(x) = 3x^2 - 12x, what is the sum of the zeros?
A. 4
B. 12
C. 0
D. 6
Show Answer & Explanation
Correct Answer: A
The sum of the zeros of a quadratic polynomial ax^2 + bx has the formula -b/a. Here it is -(-12)/3 = 4.
Q7
Medium
What is the product of the zeros of the polynomial f(x) = x^2 + 4x + 4?
A. 4
B. 0
C. 16
D. 8
Show Answer & Explanation
Correct Answer: A
The product of the zeros of a quadratic polynomial ax^2 + bx + c is given by c/a. Here, it is 4/1 = 4.
Q8
Hard
Given the polynomial p(x) = 2x^4 - 8x^3 + 6x^2, what is the value of x for which p(x) = 0?
A. 0, 1, 3
B. 0, 2, 3
C. 1, 2, 4
D. 0, 2, 4
Show Answer & Explanation
Correct Answer: B
Factoring out 2x^2 gives p(x) = 2x^2(x^2 - 4x + 3), which has roots at x = 0, x = 2, and x = 3.
Q9
Hard
If the polynomial f(x) = x^3 + ax^2 + bx + c has 3 distinct real roots, what condition must be satisfied by the coefficients a, b, and c?
A. a^2 - 4b < 0
B. a^2 - 4b = 0
C. a^2 - 4b > 0
D. b^2 - 4ac < 0
Show Answer & Explanation
Correct Answer: C
For a cubic polynomial to have 3 distinct real roots, the discriminant must be positive, which means a^2 - 4b > 0.
Q10
Hard
The polynomial g(x) = x^4 - 5x^3 + 6x^2 can be expressed in factored form. What is one of its factors?
A. (x - 2)
B. (x + 1)
C. (x - 3)
D. (x - 1)
Show Answer & Explanation
Correct Answer: D
By checking for roots, substituting x=1 gives g(1) = 0, indicating (x - 1) is a factor.

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Polynomials — Class 10 Mathematics Practice Questions Online

This page contains 1551 practice MCQs for the chapter Polynomials in Class 10 Mathematics. The questions are organized by difficulty — 581 easy, 693 medium, 277 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.