Solving Quadratics by Factorisation

• Write ax² + bx + c = 0 in standard form.
• Split the middle term or use identities to factorise.
• Apply zero-product rule: if AB = 0, then A = 0 or B = 0.

1. Standard form — ax² + bx + c = 0, a ≠ 0.
2. Factorisation — express as (px + q)(rx + s) = 0.
3. Zero-product rule — set each factor to zero.
4. Splitting — find two numbers with product ac and sum b.
5. NCERT examples — x² − 5x + 6 = 0 → (x−2)(x−3) = 0 → x = 2, 3.

Solve x² − 5x + 6 = 0 by factorisation

x² − 5x + 6 = 0
Numbers: −2 and −3 (product 6, sum −5)
(x − 2)(x − 3) = 0
x = 2 or x = 3

• Not setting equation to zero before factorising.
• Wrong pair for splitting (check product = ac and sum = b).
• Dividing by x and losing the root x = 0.

• Solve x² + x − 6 = 0 by factorisation.
• Factorise 2x² − 7x + 3.
• How many roots can a quadratic have?

Open the Practice tab for graded questions on Solving Quadratics by Factorisation.