A Polynomial | P(x)+xP(x+1)=x^2+x-1

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Easier method(I don't know if it actually works in this way)
P(x) + xP(x+1) = x² + x - 1
So,
P(x) + xP(x+1) = (x-1) + x*[(x-1) +1]
So we get P(x) = x-1

adritobiswas
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I understand that we assume that the polynomial is with degree of 1 because otherwise there should be in the right hand side something with power more than 2. I still think it should have been mentioned 🙂

natanytzhaki