📘 Class 9 · Mathematics

Chapter 2: Polynomials and Factorisation

6 lessons

Polynomials and Factorisation introduces formal vocabulary — degree, coefficients, linear/quadratic/cubic — alongside two new tools: the Remainder Theorem and the Factor Theorem, which turn Class 8's factorisation into a method that works for higher-degree expressions.

Testing p(a) when the actual factor is (x+a) — which requires testing p(−a) instead — is a frequent sign error with the Factor Theorem: to check whether (x+2) divides p(x), the correct test is p(−2)=0, not p(2)=0. This chapter is a direct prerequisite for Class 10's Polynomials (finding zeroes and their relationship to coefficients) and for solving quadratic equations by factorisation.

1
Introduction to Polynomials
Polynomials, their degree and types.
 2
Exercise 2.1 — Types and Degree
Problems on types and degree of polynomials.
 3
Exercise 2.2 — Zeroes of a Polynomial
Understanding and finding zeroes of a polynomial.
 4
Exercise 2.3 — Remainder Theorem
Division of polynomials and the remainder theorem.
 5
Exercise 2.4 — Factor Theorem
Factor theorem and its applications.
 6
Exercise 2.5 — Algebraic Identities
Important algebraic identities and their applications.