Answer
$6,\quad-7,\quad 2,\quad 3$
Work Step by Step
1. The factors of P have degrees 2, 3 and 1, so the degree of P is 2+3+1=6
2. The third factor yields the zero $-7$
3. The zero x=0 corresponds to a factor of degree 2, so its multiplicity is 2.
The zero x=4 corresponds to a factor of degree 3, so its multiplicity is 3.