A polynomial is denoted by $f(x)$. The coefficients of the polynomial are positive integers. $$f(1) =17$$ $$f(20)=421350$$ Could you tell if such a polynomial is possible? If ye, find the degree of the polynomial and also it's coefficients.
My inference:Using $f(20)=421350$ we can determine, that the degree of the polynomial cannot exceed $4$. Also since every coefficient is positive, therefore each individual coefficient $< 17$. The constant coefficient independent of $x$ is $10$. Since $421350$-constant term should be divisible by $20$.