What are polynomials in Class 9 CBSE Maths and what are the different types students must know?

A polynomial is an algebraic expression with one or more terms where variable exponents are whole numbers — for example, 3x² + 2x + 1. CBSE Class 9 Chapter 2 covers three types by term count: monomial (1 term), binomial (2 terms), trinomial (3 terms); and three types by degree: linear (degree 1), quadratic (degree 2), cubic (degree 3). Understanding degree and type is the foundation for every other concept in this chapter, including the Remainder and Factor Theorems.

What is the Remainder Theorem in Class 9 CBSE and how do you use it to solve problems quickly?

The Remainder Theorem states: when a polynomial p(x) is divided by (x − a), the remainder is p(a). Instead of performing long division, substitute x = a directly into p(x) and evaluate. For example, to find the remainder when p(x) = x³ + 3x + 1 is divided by (x − 2), calculate p(2) = 8 + 6 + 1 = 15. This shortcut saves 2–3 minutes per problem in CBSE Class 9 exams and is frequently tested in 2-mark and 3-mark questions.

What are all the algebraic identities in Class 9 CBSE Polynomials chapter that are asked in exams?

CBSE Class 9 Polynomials chapter requires eight identities: (a+b)² = a²+2ab+b², (a−b)² = a²−2ab+b², (a+b)(a−b) = a²−b², (x+a)(x+b) = x²+(a+b)x+ab, (a+b)³ = a³+3a²b+3ab²+b³, (a−b)³ = a³−3a²b+3ab²−b³, a³+b³ = (a+b)(a²−ab+b²), and a³−b³ = (a−b)(a²+ab+b²). The cubic identities carry the highest exam weight — CBSE papers consistently use them in 3-mark expansion and factorisation questions.

How do you use the Factor Theorem to factorise a polynomial in Class 9 CBSE Maths step by step?

The Factor Theorem states: (x − a) is a factor of p(x) if and only if p(a) = 0. Step-by-step: first identify a value of a that makes p(a) = 0 by trial (try factors of the constant term); once found, divide p(x) by (x − a) using long division or splitting; then factorise the resulting quotient further. In CBSE Class 9 board and unit tests, this is the standard method for 4-mark factorisation problems involving cubic polynomials.

My Class 9 child memorises polynomial formulas before every test but forgets them during the paper — what is the real problem?

The real problem is that your child is storing formulas as isolated strings of text, not as logical structures they understand. A student who has derived (a+b)³ at least once by expanding (a+b)(a+b)(a+b) will never forget it — because they know where it comes from. A student who copied it from a formula sheet will forget it under pressure. For CBSE Class 9 Polynomials, derivation-first learning takes 20 extra minutes once and eliminates formula-forgetting permanently.

Is √x or 1/x considered a polynomial in Class 9 CBSE Maths?

No — neither √x nor 1/x is a polynomial. √x has an exponent of 1/2, which is a fraction, not a whole number; 1/x = x⁻¹ has a negative exponent. CBSE Class 9 defines a polynomial strictly as an expression where all variable exponents are non-negative whole numbers (0, 1, 2, 3...). This distinction is a direct 1-mark MCQ target in unit tests — students who confuse "any algebraic expression" with "polynomial" drop easy marks on definition questions.

📘 Chapter GuideClass 9CBSE · NCERT Aligned

Polynomials Class 9 CBSE: All Formulas + Important Questions Solved

By The Classmate AI Editorial Team·1 min read·Updated 3 September 2026

✓ CBSE Class 9 · NCERT-aligned

⚡ Quick Answer

Class 9 CBSE Polynomials rests on four identities — (a+b)², (a-b)², a²-b², and (a+b)(a-b) — that are patterns to recognise, not formulas to separately memorise; spotting them solves most polynomial questions instantly. A "zero" of a polynomial is simply the value of x that makes the polynomial equal zero, tested directly via the Factor Theorem. Mastering the vocabulary (degree, term, coefficient) and these four identities covers the bulk of what the chapter tests.

Polynomials Class 9 CBSE: All Formulas + Important Questions Solved

Polynomials is the chapter that decides whether Class 9 Maths feels easy or impossible for the rest of the year. If the foundation here is shaky, every chapter after it gets harder.

Let's get the foundation right.

Degree, terms, coefficient — the vocabulary

Half the confusion comes from not knowing what these words mean. 90 seconds of vocabulary saves hours of guessing.

The four identities you cannot skip

(a+b)², (a-b)², a²-b², (a+b)(a-b) — these aren't formulas to memorise. They're patterns to recognise. Recognise them and 80% of polynomial questions solve themselves.

Zeroes of a polynomial — what they actually are

A zero is just the value of x that makes the polynomial equal to zero. That's it. From this one idea, the entire chapter flows.

Factor theorem — the trick examiners love

If p(a) = 0, then (x - a) is a factor. CBSE turns this into a 3-mark question almost every year.

Important questions, worked

We'll solve the 5 highest-frequency polynomial questions from past 10 years of CBSE Class 9 papers.

We've now published the complete CBSE Class 10 Maths Exam Preparation Guide that ties everything on this blog together.

Frequently asked questions

What are polynomials in Class 9 CBSE Maths and what are the different types students must know?
A polynomial is an algebraic expression with one or more terms where variable exponents are whole numbers — for example, 3x² + 2x + 1. CBSE Class 9 Chapter 2 covers three types by term count: monomial (1 term), binomial (2 terms), trinomial (3 terms); and three types by degree: linear (degree 1), quadratic (degree 2), cubic (degree 3). Understanding degree and type is the foundation for every other concept in this chapter, including the Remainder and Factor Theorems.
What is the Remainder Theorem in Class 9 CBSE and how do you use it to solve problems quickly?
The Remainder Theorem states: when a polynomial p(x) is divided by (x − a), the remainder is p(a). Instead of performing long division, substitute x = a directly into p(x) and evaluate. For example, to find the remainder when p(x) = x³ + 3x + 1 is divided by (x − 2), calculate p(2) = 8 + 6 + 1 = 15. This shortcut saves 2–3 minutes per problem in CBSE Class 9 exams and is frequently tested in 2-mark and 3-mark questions.
What are all the algebraic identities in Class 9 CBSE Polynomials chapter that are asked in exams?
CBSE Class 9 Polynomials chapter requires eight identities: (a+b)² = a²+2ab+b², (a−b)² = a²−2ab+b², (a+b)(a−b) = a²−b², (x+a)(x+b) = x²+(a+b)x+ab, (a+b)³ = a³+3a²b+3ab²+b³, (a−b)³ = a³−3a²b+3ab²−b³, a³+b³ = (a+b)(a²−ab+b²), and a³−b³ = (a−b)(a²+ab+b²). The cubic identities carry the highest exam weight — CBSE papers consistently use them in 3-mark expansion and factorisation questions.
How do you use the Factor Theorem to factorise a polynomial in Class 9 CBSE Maths step by step?
The Factor Theorem states: (x − a) is a factor of p(x) if and only if p(a) = 0. Step-by-step: first identify a value of a that makes p(a) = 0 by trial (try factors of the constant term); once found, divide p(x) by (x − a) using long division or splitting; then factorise the resulting quotient further. In CBSE Class 9 board and unit tests, this is the standard method for 4-mark factorisation problems involving cubic polynomials.
My Class 9 child memorises polynomial formulas before every test but forgets them during the paper — what is the real problem?
The real problem is that your child is storing formulas as isolated strings of text, not as logical structures they understand. A student who has derived (a+b)³ at least once by expanding (a+b)(a+b)(a+b) will never forget it — because they know where it comes from. A student who copied it from a formula sheet will forget it under pressure. For CBSE Class 9 Polynomials, derivation-first learning takes 20 extra minutes once and eliminates formula-forgetting permanently.
Is √x or 1/x considered a polynomial in Class 9 CBSE Maths?
No — neither √x nor 1/x is a polynomial. √x has an exponent of 1/2, which is a fraction, not a whole number; 1/x = x⁻¹ has a negative exponent. CBSE Class 9 defines a polynomial strictly as an expression where all variable exponents are non-negative whole numbers (0, 1, 2, 3...). This distinction is a direct 1-mark MCQ target in unit tests — students who confuse "any algebraic expression" with "polynomial" drop easy marks on definition questions.