Use the factor Theorem to factor polynomial.

-4 is one root

Performing synthetic division, we have

-4     1   4   -7   -34    -24

            -4          28     24

         1  0   -7     -6       0

The polynomial  is reduced to   x^3 - 7x - 6

3 is also a root.......performing synthetic division again, we have

3   1   0    -7      -6

         3      9       6

     1  3      2       0

And the remaining polynomial is   x^2 + 3x + 2   which has zeros of  -1, -2

So the factorization of the original polynomial is

P(x) = (x + 4) (x - 3) (x + 1) (x + 2)