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Polynomials Practice Questions

Class 9 · Mathematics · 2612 free MCQs with instant results and detailed explanations.

2612
Total
804
Easy
1304
Medium
504
Hard

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Topics in Polynomials

Zeros of a Polynomial 504
Remainder Theorem 478
Polynomials in One Variable 585
Algebraic Identities 527
Factor Theorem 518

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 4x^3 - 5x^2 + 6?
A. 3
B. 2
C. 1
D. 0
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is the highest power of the variable. Here, the highest power is 3 from 4x^3.
Q2
Easy
Which of the following is not a polynomial?
A. 3x^2 + 2x - 1
B. 5x^3
C. 2/x + 3
D. x^4 - 2x
Show Answer & Explanation
Correct Answer: C
A polynomial cannot have negative or fractional exponents. The term 2/x can be rewritten as 2x^(-1), which is not allowed.
Q3
Easy
Which of the following polynomials is a quadratic polynomial?
A. x^3 - 5x + 6
B. 4x^2 + 3
C. 2x
D. x^4 - x^2 + 1
Show Answer & Explanation
Correct Answer: B
A quadratic polynomial is of degree 2. The polynomial 4x^2 + 3 has the highest exponent as 2.
Q4
Medium
What is the degree of the polynomial 4x^3 - 3x^2 + 2x - 1?
A. 3
B. 2
C. 1
D. 0
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is the highest power of the variable. Here, the highest power is 3.
Q5
Medium
Which of the following represents a polynomial function?
A. f(x) = 2x^2 + 3x + 5
B. g(x) = √x + 5
C. h(x) = 1/x + 2
D. k(x) = 7 - 4√x
Show Answer & Explanation
Correct Answer: A
A polynomial function consists only of non-negative integer powers of x. Option A fits this definition.
Q6
Medium
Which polynomial is equivalent to 2(x + 3) - 3(x - 1)?
A. x + 9
B. x + 3
C. 5x + 9
D. -x + 9
Show Answer & Explanation
Correct Answer: D
Distributing gives 2x + 6 - 3x + 3, simplifying to -x + 9.
Q7
Medium
If the polynomial is in the form ax^2 + bx + c, which value of 'b' makes the polynomial symmetric about the y-axis?
A. 0
B. 1
C. -1
D. Any non-zero value
Show Answer & Explanation
Correct Answer: A
For symmetry about the y-axis, the linear term must be zero, hence b must be 0.
Q8
Hard
If p(x) = 2x^3 - 3x^2 + 4x - 5, what is p(2)?
A. 9
B. 11
C. 13
D. 15
Show Answer & Explanation
Correct Answer: B
To find p(2), substitute x with 2 in the polynomial and calculate the value.
Q9
Hard
What is the degree of the polynomial q(x) = 5x^4 - 2x^2 + 7x + 1?
A. 4
B. 2
C. 3
D. 1
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is determined by the highest power of x present in the expression.
Q10
Hard
Which of the following is a factor of the polynomial r(x) = x^3 - 6x^2 + 11x - 6?
A. (x - 1)
B. (x - 2)
C. (x - 3)
D. (x - 4)
Show Answer & Explanation
Correct Answer: C
To determine the factors, we can use the Remainder Theorem or synthetic division. Testing (x - 3) yields a remainder of 0.

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Polynomials — Class 9 Mathematics Practice Questions Online

This page contains 2612 practice MCQs for the chapter Polynomials in Class 9 Mathematics. The questions are organized by difficulty — 804 easy, 1304 medium, 504 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 5 topics, giving you comprehensive coverage of the entire chapter.