Steps to factoring polynomials

Question

What would be the steps to factor this polynomial: (6x^3+24x^2-2x-8)/(x+4)

Answer 1

A factor by grouping approach works for the numerator.

6 x^3 + 24 x^2           - 2 x – 8

6 x^2 ( x +4 )        -  2 ( x +4)             see that (x +4) appears in both groups so

(x + 4 ) ( 6 x^2 -2)

Since the denominator is x + 4,    it cancels the x + 4 in the numerator leaving

 6 x^2 -2   which factors as 2 ( sqrt(3) x -1 )( sqrt(3) +1)