Class 9 Maths - ICSE
Factorisation
The Factorisation chapter in Class 9 ICSE Mathematics builds upon algebraic identities learned in earlier grades, teaching students how to break down complex algebraic expressions into simpler multiplicative factors. This chapter is foundational for advanced algebra, fractions, and quadratic equations in Class 10. Students will learn various techniques including taking out common factors, grouping, using standard algebraic identities, and splitting the middle term of quadratic polynomials. Mastery of factorisation is essential for scoring well in the ICSE board exams, as simplified forms are frequently required in calculus, trigonometry, and word problems throughout high school mathematics.
Start Learning FreeKey Concepts
Factorisation by Common Factors
This method involves identifying the highest common factor (HCF) among all terms in an expression and factoring it out using the distributive law.
Factorisation by Grouping
When all terms do not have a direct common factor, terms are rearranged and grouped in pairs so that each group has a common binomial factor.
Factorisation using Standard Identities
Expressions that fit standard algebraic formulas like difference of squares or perfect squares are factored directly by recognizing their expansion patterns.
Splitting the Middle Term
A technique used for quadratic polynomials of the form ax² + bx + c, where the middle term bx is split into two parts whose product equals ac and sum equals b.
Factor Theorem
If a polynomial f(x) is divided by (x - a) and the remainder f(a) is zero, then (x - a) is a factor of f(x).
Important Formulas
Board Exam Info
In the ICSE Class 9 Mathematics examination, questions from Factorisation typically carry around 6 to 10 marks. They frequently appear as direct factorisation problems using splitting the middle term or identities, and as multi-step simplification questions in Section B of the paper.
Frequently Asked Questions
How do I know which method of factorisation to use first?
Always check for a common factor across all terms first. If none exists, count the number of terms: 4 terms usually mean grouping, 3 terms mean splitting the middle term or identities, and 2 terms usually mean the difference of squares.
How do I split the middle term correctly when negative signs are involved?
Carefully track the signs of the product (ac) and sum (b). List the factors of ac and check their signs to ensure they multiply to ac and add up precisely to b, keeping the signs of the larger factor in mind.
Is the Factor Theorem applicable to all polynomials in Class 9?
Yes, the Factor Theorem is extremely useful in Class 9 for finding linear factors of cubic polynomials by trial and error before applying synthetic division or long division.
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