ID016 · Algebraic identities · Classes 9–10
Factorization identities
Identities run backwards to factorise. For x² + bx + c, find two numbers that add to b and multiply to c.
x² + bx + cFactorization identities
📐 Formula
x² + (p + q)x + pq = (x + p)(x + q)
✏️ Worked example
x² + 5x + 6: 2 + 3 = 5 and 2 × 3 = 6, so x² + 5x + 6 = (x + 2)(x + 3).
🌍 Where it is used
Solving quadratic equations and simplifying fractions.
❓ Quick check
Factorise x² + 7x + 10.
🏋️ Practice
EasyFactorise x² + 4x + 3.
Answer: (x + 1)(x + 3)
MediumFactorise x² − x − 12.
Answer: (x − 4)(x + 3)
ChallengeFactorise x² − 10x + 21.
Answer: (x − 3)(x − 7)