Question

Is it possible to factor `y=x^3 - 3x^2 - 4x + 12`? If so, what are the factors?

Answer 1

(x - 3 )(x - 2 )(x + 2 )

Explanation:

By factorising in pairs :

`[ x^2 ( x - 3 ) ] + [ - 4 ( x - 3 ) ]`

ie `x^2 (x - 3 ) - 4 ( x - 3 )`

now there is a common factor of (x - 3 )

`(x - 3 )(x^2 - 4 )`

`x^2 - 4` is a difference of 2 squares.

and `x^2 - 4 = ( x - 2 )(x + 2 )`

`rArr x^3 -3x^2 - 4x + 12 = (x - 3 )(x - 2 )(x + 2 )`