α β γ Remainder Thm: p(a) Factor: p(a)=0 ⟹ (x−a) (a+b)²=a²+2ab+b² a³+b³+c³−3abc
p(x)
Chapter 2  ·  Class IX Mathematics  ·  MCQ Practice

MCQ Practice Arena

Polynomials

Zeroes, Factors and Identities — Build the Algebra Foundation That Carries You Forward

📋 50 MCQs ⭐ 26 PYQs ⏱ 60 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
20Easy
22Medium
8Hard
26PYQs
60 secAvg Time/Q
7Topics
Easy 40% Medium 44% Hard 16%

Why Practise These MCQs?

CBSE Class IXNTSEState Boards

Polynomials in Class IX focuses on terminology (degree, coefficient, zero), the Remainder and Factor Theorems, and algebraic identities. These MCQs are direct and formula-driven — 70% can be solved by substitution or identity application. CBSE exams award 1–2 MCQs from this chapter; NTSE uses factor theorem and identity-based reasoning. The five key identities alone cover 30% of all questions.

Topic-wise MCQ Breakdown

Definitions: Degree, Terms, Coefficients6 Q
Types of Polynomials (Linear/Quad/Cubic)5 Q
Zeroes of a Polynomial8 Q
Remainder Theorem10 Q
Factor Theorem8 Q
Algebraic Identities (5 key identities)10 Q
Factorisation of Polynomials3 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$(a+b)^2 = a^2+2ab+b^2$
$(a-b)^2 = a^2-2ab+b^2$
$a^2-b^2 = (a+b)(a-b)$
$(a+b)^3 = a^3+3a^2b+3ab^2+b^3$
$(a-b)^3 = a^3-3a^2b+3ab^2-b^3$
$a^3+b^3+c^3-3abc = (a+b+c)(a^2+b^2+c^2-ab-bc-ca)$
$p(a) = 0 \Rightarrow (x-a)\ \text{is a factor (Factor Theorem)}$

MCQ Solving Strategy

Remainder Theorem MCQs: to find remainder when p(x) is divided by (x−a), simply compute p(a). Factor Theorem: (x−a) is a factor if and only if p(a) = 0 — test by substitution. For identity MCQs, recognise the pattern first (is it a²−b²? a cubic? a+b+c form?) then substitute. For degree MCQs, the degree is the highest power of the variable — ignore coefficients.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Identify degree and type, find zeroes by substitution, apply (a+b)² and a²−b²

② Medium

Remainder theorem with quadratics/cubics, factor theorem to find k

③ Hard

Cubic factorisation, a³+b³+c³−3abc identity, multi-step simplification

★ PYQ

CBSE — remainder + factor theorem; NTSE — identity-based computation

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 📘✔️ Exercises Step-by-step NCERT solutions ✔️❌ True / False Concept-based True & False ➡ Next Chapter Coordinate Geometry
🎯 Knowledge Check

Maths — Polynomials

50 Questions Class 9 MCQs
1
Which of the following is a polynomial?
2
What is the degree of the polynomial \(5x^3 + 4x^2 - 3x + 1\)?
3
Which of the following is a binomial?
4
What is the sum of the coefficients of the polynomial \(3x^2 + 5x – 7\)?
5
Which of the following is a polynomial of degree 2?
6
The coefficient of \(x^2\) in the polynomial \(x^3 + 4x^2 - 7x + 2\) is:
7
What is the degree of the polynomial \(2x^5 - 3x^4 + 4x^2 + 1\)?
8
Which of the following is a monomial?
9
The degree of the polynomial \(7x^4 - 3x^2 + 5x – 6\) is:
10
Which of the following polynomials is a perfect square trinomial?
11
Which of the following is a factor of \(x^2 – 4\)?
12
The product of two polynomials is always:
13
The roots of the polynomial \(x^2 - 5x + 6\) are:
14
Which of the following is a factor of \(x^2 – 9\)?
15
If \(x + 2\) is a factor of the polynomial \(x^2 + bx + c\), then the value of \(b\) is:
16
What is the sum of the roots of the polynomial \(x^2 - 5x + 6\)?
17
What is the product of the roots of the polynomial \(x^2 - 7x + 12\)?
18
Which of the following is the factorization of \(x^2 - 4x – 5\)?
19
Which of the following is a polynomial with three terms?
20
If the polynomial \(x^2 + 3x + 2\) is divided by \(x + 1\), the remainder is:
21
The factorization of \(x^2 – 16\) is:
22
The polynomial \(3x^2 - 2x + 1\) is:
23
What is the degree of the polynomial \(6x^4 - 3x + 2\)?
24
Which of the following is a constant polynomial?
25
What is the result of dividing \(x^2 – 9\) by \(x + 3\)?
26
Which of the following polynomials is a cubic polynomial?
27
If \(x – 3\) is a factor of \(x^2 + x – 6\), the other factor is:
28
What is the sum of the squares of the roots of \(x^2 - 6x + 9\)?
29
Which of the following is the factorization of \(x^2 + 3x – 10\)?
30
What is the value of the polynomial \(2x^2 + 3x – 4\) at \(x = 2\)?
31
The roots of the polynomial \(x^2 – 9\) are:
32
Which of the following is the factorization of \(x^2 + 6x + 9\)?
33
The polynomial \(2x^3 - x^2 + 5x – 3\) is of degree:
34
What is the result of \(3x^2 + 5x – 7\) when \(x = -1\)?
35
The polynomial \(x^2 - 4x + 3\) is a:
36
Which of the following is a factor of \(x^2 + 4x + 3\)?
37
Which of the following is a polynomial of degree 4?
38
What is the sum of the coefficients of the polynomial \(3x^3 - 2x^2 + 4x – 5\)?
39
The polynomial \(x^2 - 4x + 3\) can be factored as:
40
What is the degree of the polynomial \(x^5 - 3x^2 + 2x – 4\)?
41
Which of the following is the factorization of \(x^2 + 6x + 9\)?
42
If the sum of the roots of the quadratic polynomial \(x^2 - 4x + 3\) is 4, then the roots are:
43
The factorization of \(x^2 + 7x + 10\) is:
44
The polynomial \(x^3 - x^2 + 3x – 3\) can be factored as:
45
The value of \(x^2 - 2x + 5\) at \(x = 3\) is:
46
What is the product of the roots of the polynomial \(x^2 - 7x + 12\)?
47
The roots of the polynomial \(x^2 + 2x + 1\) are:
48
Which of the following polynomials has a degree of 5?
49
If x+4x + 4 is a factor of \(x^2 + 7x + 12\), the other factor is:
50
The polynomial \(x^2 - 3x – 4\) can be factored as:
📚
ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
Sharing this chapter
NCERT Class 9 Maths Chapter 2 Polynomials MCQs
NCERT Class 9 Maths Chapter 2 Polynomials MCQs — Complete Notes & Solutions · academia-aeternum.com
This set of multiple-choice questions is based on the topic Introduction to Polynomials. The questions cover key concepts such as types of polynomials (monomials, binomials, trinomials), polynomial expressions, zeroes of polynomials, the Factor Theorem, and essential algebraic identities. These MCQs are designed to test your understanding and application of fundamental ideas in polynomials, helping to strengthen your algebraic foundation.
🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
Share on
WhatsApp
Telegram
X / Twitter
Facebook
Instagram
Threads
Pinterest
LinkedIn
Quora
Discord
Reddit
Email
academia-aeternum.com/class-9/mathematics/polynomials/mcqs/ Copy link
💡
Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

Academia Aeternum is an online educational platform providing NCERT based notes, MCQs, quizzes, and conceptual explanations for students from Class 9 to Class 12 and competitive exam aspirants.

The platform provides structured learning resources for Mathematics, Physics, Chemistry, Biology, and Computer Science aligned with the NCERT curriculum.

Yes. Many MCQs are designed in patterns similar to JEE, NEET, and other entrance exams to improve analytical thinking and exam readiness.

Yes. Most study materials are derived directly from NCERT textbooks to ensure alignment with school curriculum and board examination requirements.

Yes. Students can access learning materials, MCQs, and revision resources freely without subscription.

MCQs improve accuracy, speed, and conceptual clarity while helping students practice objective questions commonly asked in exams.

Yes. Each question is accompanied by a clear explanation to help students understand the reasoning behind the correct answer.

Yes. Teachers can use the questions and explanations for classroom discussions, worksheets, and quick revision exercises.

Yes. The structured format and clear explanations make it ideal for independent learning.

Yes. Concise notes and MCQ practice sets allow students to revise important concepts quickly.

Yes. Explanations are written in clear student friendly language for easy understanding.

Yes. Questions range from basic conceptual understanding to advanced application based problems.

New chapters, questions, and quizzes are regularly added to expand the learning resources.

Yes. Consistent practice improves concept retention, problem solving ability, and exam confidence.

Regular objective practice helps students identify weak areas, improve speed, and prepare effectively for competitive examinations.

Recent Posts

    --:-- ⏱ Time
    ⚡ Progress 0 / 50 answered

    Polynomials — Learning Resources

    📄 Detailed Notes
    ✔️ True / False
    📌 Exercise
    📝 Exercises
    Exercise 2.1 Exercise 2.2 Exercise 2.3 Exercise 2.4
    📚
    ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025
    Sharing this chapter
    NCERT Class 9 Maths Chapter 2 Polynomials MCQs
    NCERT Class 9 Maths Chapter 2 Polynomials MCQs — Complete Notes & Solutions · academia-aeternum.com
    This set of multiple-choice questions is based on the topic Introduction to Polynomials. The questions cover key concepts such as types of polynomials (monomials, binomials, trinomials), polynomial expressions, zeroes of polynomials, the Factor Theorem, and essential algebraic identities. These MCQs are designed to test your understanding and application of fundamental ideas in polynomials, helping to strengthen your algebraic foundation.
    🎓 Class 9 📐 Mathematics 📖 NCERT ✅ Free Access 🏆 CBSE · JEE
    Share on
    WhatsApp
    Telegram
    X / Twitter
    Facebook
    Instagram
    Threads
    Pinterest
    LinkedIn
    Quora
    Discord
    Reddit
    Email
    academia-aeternum.com/class-9/mathematics/polynomials/mcqs/ Copy link
    💡
    Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

    Get in Touch

    Let's Connect

    Questions, feedback, or suggestions?
    We'd love to hear from you.