Question

How do you factor `y= 2x^2 - 9x – 18` ?

Answer 1

`y = (2x +3)(x - 6)`

Explanation:

If the factored quadratic is expressed as `(ax +b)(cx+d)` then the general form of a quadratic is `y = acx^2 +(bc + ad)x +bd`
We therefore need to look for factors of `2` and `(-18)` that will combine to give `(-9)`
Possible factors of `2` are only `2` and `1`
Possible factors of `(-18)` are `-9` and `2` or `-6` and `3`
`2*(-6) +1*3 = -9` so these are the correct factors.
Hence `y = (2x +3)(x - 6)`