An Intriguing Integral

Calculus Level 4

f(x)f(x) is a polynomial that satisfies f(x+y)=f(x)+f(y)+3xyf(x+y) = f(x) + f(y) + 3xy for all real numbers xx and yy. If f(0)=35f'(0) = 35, what is the value of f(2)f(2)?

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