If $$f(x) = (x - 2)(x^2 + Px + 4)$$ and $$(x - 3)$$ is a factor of $$f(x)$$, then what is the value of $$P$$?

If $$f(x) = (x - 2)(x^2 + Px + 4)$$ and $$(x - 3)$$ is a factor of $$f(x)$$ Let say, (x-m) is another factor of f(x).

So, $$\left(x-3\right)\left(x-m\right)=x^2+Px+4$$

or, $$\left(x^2-3x-mx+3m\right)=\left(x^2+Px+4\right).$$

or, $$-x\left(3+m\right)+3m=Px+4.$$

So, by comparing both side , we can say that :

$$-\left(3+m\right)=P\ \ and\ \ 3m=4.$$

or, $$m=\frac{4}{3}.$$

So, $$P=-3-\frac{4}{3}=\frac{-9-4}{3}=\frac{-13}{3}.$$

C is correct choice.