Question

How do you factor `12x^2-4x-40`?

Answer 1

`color(blue)((12x + 20 ) (x-2)` is the factorised form of the expression.

Explanation:

`12x^2 - 4x - 40`

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 = 12*(-40) = -480`

AND

`N_1 +N_2 = b = -4`

After trying out a few numbers we get `N_1 = 20` and `N_2 =-24`
`20 *(- 24) = - 480`, and `20+(-24)= -4`

`12x^2 - 4x - 40 = 12x^2 - 24 x + 20x - 40`

`= 12x(x-2) + 20 ( x-2)`

`(x-2)` is a common factor to each of the terms
`color(blue)((12x + 20 ) (x-2)` is the factorised form of the expression.