Q1
What does factorisation mean?
AExpressing an expression as a product of factors
BExpanding an expression
CAdding terms together
DNothing specific
ICSEClass 9 (ICSE)MathematicsCh 5 · Topic 1
Factorisation
Factorisation expresses an algebraic expression as a product of factors, using methods like common factors, identities, or grouping.
Core concept
The common factor method finds the greatest common factor of all terms and factors it out, like 4x+8 = 4(x+2).
How it works
Factorisation using identities recognises patterns, like a²-b² factoring to (a+b)(a-b), or a²+2ab+b² factoring to (a+b)².
Why it matters
Factorisation by grouping involves grouping terms to find common factors, useful for expressions with four or more terms.
Key detail
Trinomial factorisation, like x²+7x+12, finds two numbers that multiply to 12 and add to 7, giving (x+3)(x+4).
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Quick notes
• Common factor method factors out the GCF.
• 4x+8 = 4(x+2).
• Identities help factorise, like a²-b²=(a+b)(a-b).
• a²+2ab+b² factors to (a+b)².
• Grouping factors expressions with 4+ terms.
• Trinomials factor by finding matching numbers.
• x²+7x+12 = (x+3)(x+4), since 3×4=12, 3+4=7.
• Different methods suit different expressions.