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 c
- add to give b
- Write down the brackets (x + p)(x + q) – that’s your answer!
Don’t forget – both p and q here can be negative!
Make sure you know if you are being asked to:
- Solve an equation (look for the “=”) or
- Factorise an expression (no “=”)
Do not confuse the two things.
When the quadratic expression only has two terms check for:
- Simple factorisation (no number term, ie. when c = 0 )
- Difference Of Two Squares (no x term, ie. when b = 0)