Factor the polynomial completely y^3+6y^2-4y-24

You might try factoring by grouping first.

Note that y^3+6y^2 = y^2(y+6), and that -4y-24 = -4(y+6).  So, (y+6) is a factor common to the first group of 2 terms and the 2nd grp of 2 terms.

We get  (y+6)[y^2 - 4].  Note that y^2-4 is easily factorable:  (y-2)(y+2),
so we now have three factors of the original poly:

(y+6), (y-2) and (y+2)   (answer)