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
Check for a common factor – life will be a lot easier if you take it out before you try to factorise.
If a is negative take out out a factor of -1 – that will help, too.