Question

How do you factor `2n^2 + 3n - 9`?

Answer 1

`2n^2+ 3n -9`

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like `an^2 + bn + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 2 xx (-9) = -18`
and
`N_1 +N_2 = b = 3`

After trying out a few numbers we get `N_1 = 6` and `N_2 =-3`

`6 xx (-3) = -18` and `6+(-3)= 3`

`2n^2+ 3n -9 = 2n^2+ 6n - 3n -9`

`= 2n(n +3) -3(n+3)`

`=color(green)((2n - 3)(n +3)`