ALG016 · Algebraic expressions · Classes 9–11
Polynomial division
Dividing a polynomial by (x − r) gives a quotient and a remainder. For x² + bx + c the quotient is x + (b + r) and the remainder is p(r).
÷ (x − r)Polynomial division
📐 Formula
p(x) = (x − r) q(x) + p(r)
✏️ Worked example
(x² + 5x + 6) ÷ (x + 2): quotient x + 3, remainder p(−2) = 4 − 10 + 6 = 0.
🌍 Where it is used
Factorising polynomials and simplifying algebraic fractions.
❓ Quick check
(x² − 1) ÷ (x − 1) = ?
🏋️ Practice
Easy(x² + 7x + 12) ÷ (x + 3) = ?
Answer: x + 4
MediumRemainder when x² + 1 is divided by x − 2?
Answer: 5
Challenge(x² − 9) ÷ (x + 3) = ?
Answer: x − 3