Prove <x^2+1> is maximal in R[x]

R[x] = {all polynomials with real coefficients}

<x^2+1> = {f(x)*(x^2+1) ; f(x) is from R[x]}

Could you guys give me some hints? I am not really sure how to even start this. This exact problem is actually an example in my book but I could not even follow it! (Gallian)

Thank you