Simple Concept Tough Problem - 7

Hello readers ! We are back with the 7th problem in SCTP series. The problem for today is rather simple. However, in mathematics, simple things tend to become complex all of a sudden. Let’s take it up :

Let P(x) be a polynomial with positive integer coefficients such that the product of all the coefficients is 41. The remainder when P(x) is divided by x-1 is 78. What is the degree of P(x) ?

Here is the solution :