Finding value of the function $f(x)f(y) = f(x) + f(y) + f(xy) - 2$? So here is the question 

If $f(x)$ is a polynomial satisfying $$f(x)f(y) = f(x) + f(y) + f(xy) - 2$$ for all real $x$ and $y$  and $f(3) = 10$, then $f(4)$ is equal to ?

here what i have tried

Putting $x=y=1$ in the given solution,$$(f(1)^2) = 3f(1) - 2$$ on solving it we get $$f(1) = 2$$
  or$$f(1)= 1$$ so putting $y=1$in the eqation $$f(x)f(y) = f(x) + f(y) + f(xy) - 2$$we get $$f(x) = 1$$ but it not true as $$f(3) = 10$$ so $f(1) = 2$

i am stuck here i don't know what to do next please help me
Akash
Thanks

Hint:
$$f(x)f(y)=f(x)+f(y)+f(xy)-2$$
$$f(x)(y)-f(x)-f(y)+1=f(xy)-2+1$$
$$(f(x)-1)(f(y)-1)=f(xy)-1$$
Define $g(a)=f(a)-1$ for every $a$, now we have:
$$g(x)g(y)=g(xy)$$
We know that $f$ is a polynomial, therefore $g$ is continuous. Hence ....
