Factor p(x) = x3+3x2-16x-48.

48 factors are 2,3,4,6,8,12,16. So we  see for which of
these p(x) vanishes.

Obviously, p(-3) =
-3^3+3*(-3)^2-16(-3)-48 = -9+9+48-48=0.

p(4) =
4^3+3*4^2-16*x-48 = 64+48-64-48 = 0.

So, (x+3)(x-4) are
factors of x^3+3x^2-16x-48.

So, x^3+3x^2-16x-48 =
(x+3)(x-4)(x+k). Putting x =0 we get

-48 = 3*-4*k. Or k =
-48/(-12 ) = 4.

Therefore (x+3)(x-4)(x+4) are the 3 factors
of p(x).