What is a quadratic expression?

• A quadratic expression looks like this:ax² + bx + c (as long as a ≠ 0)
• Note: If there are any higher powers of x (like x³ say) then it is not a quadratic!

Factorising a 3 term quadratic expression (a ≠ 1)

• Signs in quadratic determine signs in brackets:
  • If c is positive then both signs are the same as the sign of b
  • If c is negative then the signs are different and bigger number has the sign of b

   

• Using those signs find numbers p and q which
  • Multiply to give a × c
  • Add to give b
  • Cheat by writing brackets as (ax + p)(ax + q) – Yes, I know! This is not correct!
  • Uncheat by cancelling common factors in each bracket