Class 8 Maths - ICSE
Factorisation (ICSE)
The Chapter 'Factorisation' in Class 8 ICSE Mathematics introduces students to the reverse process of multiplication, where an algebraic expression is broken down into the product of its simpler irreducible factors. Students learn various techniques such as taking out the highest common factor, grouping terms, applying standard algebraic identities like (a+b)^2, (a-b)^2, and a^2-b^2, and splitting the middle term of quadratic polynomials. This fundamental topic is crucial as it forms the bedrock for solving linear and quadratic equations, simplifying algebraic fractions, and advanced calculus in higher ICSE board classes.
Start Learning FreeKey Concepts
Common Factor Method
Finding the Greatest Common Divisor (GCD) of numerical and literal coefficients across all terms of an expression and factoring it out using the distributive property.
Factorisation by Grouping
Rearranging terms into suitable pairs or groups so that a common binomial factor can be extracted when no single factor is common to all terms.
Using Standard Identities
Applying algebraic formulas in reverse, such as difference of squares and perfect square trinomials, to quickly factorise expressions.
Splitting the Middle Term
A technique used for quadratic expressions of the form ax^2 + bx + c, where the middle term 'bx' is split into two parts whose product equals 'ac' and sum equals 'b'.
Important Formulas
Board Exam Info
In the ICSE Class 8 Mathematics final examinations, Factorisation typically carries around 6 to 10 marks. Questions frequently appear as 2-mark direct factorisation problems using identities or grouping, and 3 to 4-mark questions involving splitting the middle term or multi-step expressions.
Frequently Asked Questions
How do I know which factorisation method to use first?
Always check for a common factor across all terms first. If none exists, look at the number of terms: 4 terms usually mean grouping, while 3 terms usually mean identities or splitting the middle term.
What is the difference between expansion and factorisation?
Expansion means multiplying terms to remove brackets and get a sum, whereas factorisation means reversing the process to write an expression as a product of factors.
How do I check if my factorised answer is correct?
Multiply the factors back together using distributive property or algebraic multiplication; if you get the original expression, your answer is correct.
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