Factorisation (NCERT Ch. 14)

• Factorise algebraic expressions using common factors.
• Factorise using grouping of terms.
• Factorise using standard identities: (a+b)², (a-b)², a²-b².
• Divide algebraic expressions by monomials and other polynomials.

1. Common factor method: find the highest common factor (HCF) of all terms and take it out (e.g., 6x + 9 = 3(2x+3)).
2. Grouping method: group terms in pairs that share a common factor, then factor each pair.
3. Key identities: (a+b)² = a² + 2ab + b²; (a-b)² = a² - 2ab + b²; a² - b² = (a+b)(a-b).
4. To divide a polynomial by a monomial, divide each term separately.

Factorise: x² - 9

This matches a² - b² with a=x, b=3.
x² - 9 = (x+3)(x-3)

• Forgetting to check for a common factor FIRST before trying other methods.
• Misapplying the (a+b)² identity by forgetting the middle 2ab term.
• Sign errors when factorising expressions with negative terms.

• Factorise: 5x + 10.
• Factorise: x² - 16.

Open the Practice tab for graded questions on Factorisation (NCERT Ch. 14).