Factorisation for Math Olympiad: Complete Preparation Guide

Why This Matters

Factorisation is the reverse of expansion, and it is one of the most satisfying mathematical skills to master. In Olympiad papers, factorisation questions test your ability to recognize patterns and break down complex expressions.

For Class 8 students, competition problems go beyond routine factoring. They test whether you can spot common factors in unusual expressions, apply algebraic identities creatively, and use factoring by grouping for complex polynomials.

Best Strategy

Common Pitfalls

Mistakes to avoid:

• Missing the common factor — Always factor out the GCF first.
• Identity misrecognition — $x^2 + 9$ is NOT $(x+3)^2$. It is $x^2 + 9$ (cannot be factored over reals).
• Sign errors in grouping — Be careful with negative signs when regrouping terms.
• Incomplete factoring — Factor completely. $x^4 - 1 = (x^2+1)(x^2-1) = (x^2+1)(x+1)(x-1)$.

Practice Questions

Try these!

Question 1

Factorise: $x^2 - 10x + 25$

Solution: This is $(x-5)^2$ using the identity $a^2 - 2ab + b^2 = (a-b)^2$.

Question 2

Factorise: $4a^2 - 9b^2$

Solution: $= (2a)^2 - (3b)^2 = (2a+3b)(2a-3b)$

Question 3

Factorise: $x^3 + 3x^2 + 3x + 1$

Solution: This is $(x+1)^3$ using the cube identity!

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