The Factor Theorem

Because f(3/2)=0, so (2x-3) is a factor.
And, (x-2) is given as a factor.

Let the third factor be (x+a)
Then, f(x)=(2x-3)(x-2)(x+a)

Because f(4)=50
So, f(4)=[2(4)-3](4-2)(4+a)=50
(5)(2)(4+a)=50
4+a=5
a=1

So, f(x)=(2x-3)(x-2)(x+1)
=2x^3 - 5x^2 - x + 6

Hope that I can help you! ^^