Question

How do you solve `x^2 - x - 12 = 0` by factoring?

Answer 1

The solutions are
`color(blue)(x=-3`
`color(blue)(x=4`

Explanation:

`x^2−x−12=0`

We can Split the Middle Term of this expression to factorise it and thereby find solutions.

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 = -1`

After trying out a few numbers we get `N_1 = 3` and `N_2 =-4`
`3*-4 = -12`, and `3+(-4)= -1`

`x^2−x−12=x^2−4x+3x−12`

`x(x-4) +3(x−4)=0`

`(x+3)(x-4)=0`

Now we equate the factors to zero.
`x+3 = 0 , color(blue)(x=-3`
`x-4 = 0 , color(blue)(x=4`