How many practice questions are available for Polynomials?

SparkEd Math offers 0+ practice questions for Polynomials across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Polynomials content free on SparkEd Math?

Yes! All Polynomials content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Polynomials differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Polynomials problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Polynomials content aligned with the CBSE syllabus?

Yes, all Polynomials questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 9. The content follows the official curriculum structure and exam pattern.

Polynomials — Class 9 CBSE (2025-26)

About Polynomials — Class 9 CBSE

Understand degree, zeroes of polynomials, remainder theorem, and factor theorem. This topic is part of the CBSE Class 9 mathematics syllabus (chapter: Chapter 2). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Polynomials — solved examples for Class 9 CBSE

Example 1easy

What is the degree of the polynomial

5x^3 + 4x^2 - 7

Step-by-step solution

The terms are $5x^3$ , $4x^2$ , and $-7$ .
The highest power of $x$ is 3.
$\text{Degree} = 3$

Answer: 3

Example 2medium

(x - 2)

is a factor of

p(x) = x^3 - 4x^2 + x + 6

, which of the following is true?

A) $p(2) = 0$
B) $p(-2) = 0$
C) $p(2) = 6$
D) $p(2) = -6$

Step-by-step solution

Factor Theorem: $(x-a)$ is a factor of $p(x)$ iff $p(a) = 0$ .
Since $(x-2)$ is a factor, $p(2) = 0$ .

Answer: $p(2) = 0$

Example 3hard

Factorise:

x^3 - 6x^2 + 11x - 6

A) $(x-1)(x-2)(x-3)$
B) $(x+1)(x-2)(x-3)$
C) $(x-1)(x+2)(x-3)$
D) $(x-1)(x-2)(x+3)$

Step-by-step solution

$p(1) = 1 - 6 + 11 - 6 = 0$ , so $(x-1)$ is a factor.
Dividing: $x^3 - 6x^2 + 11x - 6 = (x-1)(x^2 - 5x + 6)$
$x^2 - 5x + 6 = (x-2)(x-3)$
Final:
$(x-1)(x-2)(x-3)$

Answer: $(x-1)(x-2)(x-3)$

Practice questions on Polynomials

Q1.easy
Which of the following is a monomial?
1. A) $x + 1$
2. B) $3x^2$
3. C) $x^2 + x + 1$
4. D) $x - y$
Show answer
Answer: $3x^2$
Hint: A monomial has only one term.
Q2.easy
The zero of the polynomial $p(x) = 2x - 6$ is:
1. A) $-3$
2. B) $3$
3. C) $6$
4. D) $-6$
Show answer
Answer: $3$
Hint: Set $p(x) = 0$ and solve for $x$ .
Q3.easy
A polynomial of degree 2 is called a:
1. A)Linear polynomial
2. B)Quadratic polynomial
3. C)Cubic polynomial
4. D)Constant polynomial
Show answer
Answer: Quadratic polynomial
Hint: Think about the prefix 'quad' relating to the number 2.
Q4.medium
Find the remainder when $x^3 + 3x^2 + 3x + 1$ is divided by $(x + 1)$ .
1. A)8
2. B)0
3. C)1
4. D) $-1$
Show answer
Answer: 0
Hint: By Remainder Theorem, remainder = $p(-1)$ .
Q5.medium
Factorise: $x^2 - 7x + 12$
1. A) $(x-3)(x-4)$
2. B) $(x-2)(x-6)$
3. C) $(x+3)(x+4)$
4. D) $(x-1)(x-12)$
Show answer
Answer: $(x-3)(x-4)$
Hint: Find two numbers whose product is 12 and sum is $-7$ .
Q6.medium
Expand using identity: $(2x + 3y)(2x - 3y)$
1. A) $4x^2 - 9y^2$
2. B) $4x^2 + 9y^2$
3. C) $2x^2 - 3y^2$
4. D) $4x^2 - 6y^2$
Show answer
Answer: $4x^2 - 9y^2$
Hint: Use $(a+b)(a-b) = a^2 - b^2$ with $a = 2x$ and $b = 3y$ .
Q7.hard
If $x - \frac{1}{x} = 3$ , find $x^3 - \frac{1}{x^3}$ .
1. A)27
2. B)36
3. C)18
4. D)9
Show answer
Answer: 36
Hint: Use the identity $a^3 - b^3 = (a-b)(a^2 + ab + b^2)$ or $(a-b)^3 = a^3 - 3ab(a-b) - b^3$ .
Q8.hard
If $a + b + c = 0$ , find the value of $a^3 + b^3 + c^3$ .
1. A) $0$
2. B) $3abc$
3. C) $abc$
4. D) $-3abc$
Show answer
Answer: $3abc$
Hint: Use the identity $a^3 + b^3 + c^3 - 3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$ .
Q9.hard
Factorise: $x^3 + 13x^2 + 32x + 20$
1. A) $(x+1)(x+2)(x+10)$
2. B) $(x+1)(x+4)(x+5)$
3. C) $(x+2)(x+5)(x+2)$
4. D) $(x+1)(x+10)(x+2)$
Show answer
Answer: $(x+1)(x+2)(x+10)$
Hint: Try $x = -1$ first to check if it's a zero.

These are 9 of the 60 questions available for Polynomials. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.