Class 10 Maths - ICSE
Factorisation of Polynomials
The chapter Factorisation of Polynomials for Class 10 ICSE builds upon basic algebraic methods to help you break down complex polynomials into simpler linear or quadratic factors. You will master crucial techniques like the Factor Theorem and the Remainder Theorem, which allow you to find roots and factorise cubic and higher-degree polynomials without long division. This chapter is a foundational tool in algebra, carrying significant weight in ICSE board examinations. Questions from this topic regularly appear in both Section A and Section B, making it essential for scoring full marks in your mathematics paper.
Start Learning FreeKey Concepts
Remainder Theorem
If a polynomial f(x) is divided by a linear expression (x - a), the remainder is equal to f(a).
Factor Theorem
If (x - a) is a factor of a polynomial f(x), then f(a) = 0. Conversely, if f(a) = 0, then (x - a) is a factor.
Splitting the Middle Term
A method used to factorise quadratic polynomials of the form ax^2 + bx + c by breaking the middle term into two parts whose product equals ac and sum equals b.
Synthetic Division / Inspection Method
A technique used to find the first linear factor of a cubic polynomial by guessing integer values that make the polynomial zero.
Important Formulas
Board Exam Info
In the ICSE Class 10 Mathematics examination, this chapter typically carries about 4 to 6 marks. Questions usually appear as a dedicated sub-question in Section B, requiring students to completely factorise a cubic polynomial using the Factor Theorem, followed by solving an equation.
Frequently Asked Questions
How do I find the first factor of a cubic polynomial?
Use the Factor Theorem by testing factors of the constant term (the last number in the polynomial) until you find a value 'a' where f(a) = 0.
What is the difference between the Remainder Theorem and Factor Theorem?
The Remainder Theorem helps you find the leftover value when a polynomial is divided. The Factor Theorem is a special case of the Remainder Theorem where the remainder is exactly zero.
Can I use long division instead of synthetic division in the ICSE exam?
Yes, algebraic long division is fully accepted in ICSE board exams to find the remaining quadratic factor after obtaining the first linear factor.
Learn Factorisation of Polynomials with Your AI Tutor
10 different ways to study this chapter. Free for 3 chapters per day.
Lecture
Key Points
Interactive
Quiz
Flashcards