Question

How do you factor `x^2 - 4x - 12`?

Answer 1

`x^2 - 4x - 12=color(green)((x-6)(x+2)`

Explanation:

`color(red)(x^2 - 4x - 12`

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*-12 = -12`
AND
`N_1 +N_2 = b = -4`

After trying out a few numbers we get `N_1 = -6` and `N_2 =2`

`-6*2 = -12`, and `-6+(2)= -4`

`color(red)(x^2 - 4x - 12) = x^2 - 6x + 2x - 12`

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

`(x-6)` is a common factor to each of the terms

`=color(green)((x-6)(x+2)`