Finding polynomial, given one output

Sometimes, we can get a question like: Find a polynomial, such that.

$f(7)=89183, 0 leq a_i < 7$

Basically, the question asks us for the polynomial that will give as 89183, given that the coefficients are less than 7 and bigger than or equal to 0. Let’s illustrate this:

$f(7)=a*7^5+b*7^4+c*7^3+d*7^2+e*7^1+f$

Please consider that there might be more or less coefficients, this is just to facilitate the interpretation.

Probably, you might already see, that the number 89183 is in radix 10, and the number, using the coefficients, is in radix 7 $(abcdef)_7$ . When we used our polynomial to obtain the value of it, when x=7, we actually converted a number to radix 10.