F(x) is a polynomial with real coefficients such that:

F(0) = 1, and:
F(2) + F(3) = 125, and:
F(x)*F(2x²) = F(2x³ + x)

Find the value of F(5).

(In reply to Solution by Harry)

Well done, Harry.
I note Harry's solution:  1 + 2x² + x⁴  =  (1 + x²)²
is the square of a trivial solution, which solved the equation but not the boundary condition of F(2) + F(3) = 125

Posted by Larry on 2014-08-26 17:23:55