Question

let p(x)-p'(x)=x^n.then p(0) =?

Answer 1

P(x) is a polynomial with integer coefficient .
Let , P(x) = axⁿ + a1.x(n-1) + a2.x(n-2) ........... + an.1
P(n) is divisble by n , it means this is possible only when ,
if P(x) has no constant term .
example : P(x) = x³ + x² + x
if we put x = n
P(n) = n³ + n² + n
= n( n² + n +1) is divisible by n .

hence, P(0) = 0