Question

How do you factor `x^2 +3x - 18 = 0`?

Answer 1

`x^2 + 3x -18`

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like `ax^2 + bx + c`, we need to think of 2 numbers such that:

`N_1*N_2 = a*c = 1*(-18) = -18`
and,
`N_1 +N_2 = b = 3`

After trying out a few numbers we get `N_1 = 6` and `N_2 =-3`
`6*(-3) = -18` and `6+(-3)= 3`

`x^2 + 3x -18 = x^2 + 6x - 3x -18`

`x(x+6) -3(x+6)`

`color(green)((x-3)color(red)((x + 6)` is the factorised form.