Find the polynomial P(x)P(x)P(x) such that P(x)−P(x−1)=2xP(x) - P(x-1) = 2xP(x)−P(x−1)=2x for all xxx.
P(x)=x2+xP(x) = x^2 + xP(x)=x2+x
P(x)=x2−xP(x) = x^2 - xP(x)=x2−x
P(x)=2x2+xP(x) = 2x^2 + xP(x)=2x2+x
P(x)=x2+2P(x) = x^2 + 2P(x)=x2+2