If $P(x)=2x^{3}+x^{2}-13x+6$, then:
a) Verify that $(x+3)$ is a factor of $P(x)$.
b) Factorize $P(x)$ using synthetic division.
c) Find all the roots of $P(x)$.
d) Write complete factorized form of $P(x)$ and confirm by expanding.