Let $f(x)$ be a polynomial with real coefficients such that $f(0) =
1$, $f(2) + f(3) = 125,$ and for all $x$, $f(x)f(2x^2) = f(2x^3 +
x)$. Find $f(5)$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $f(x)$ be a polynomial with real coefficients such that $f(0) =
1$, $f(2) + f(3) = 125,$ and for all $x$, $f(x)f(2x^2) = f(2x^3 +
x)$. Find $f(5)$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
676
Let $f(x)$ be a polynomial with real coefficients such that $f(0) =
1$, $f(2) + f(3) = 125,$ and for all $x$, $f(x)f(2x^2) = f(2x^3 +
x)$. Find $f(5)$.
train