Question

How do you factor `y=x^3 + 8x^2 + 19x + 12` ?

Answer 1

`(x+1)(x+4)(x-3)`

Explanation:

First, use all integer negative numbers that divide the known term 12 and substitute them in x
Prove x=-1
`y=(-1)^3+8*(-1)^2+19*(-1)+12=0`
then use Ruffini method to have:

`(x^2+7x+12)(x+1)`

`x=(-7+-sqrt(49-48))/2`
`x=(-7+-1)/2`
`x=-4 and x=3`