Suppose P(x) = anxn + an-1xn-1+an-2xn-2+…+a1x1+a0 is any polynomial of degree 1 or higher with real coefficients. Show that there must exist a real number k so that if we create the new polynomial Q(x) = P(x-k), then Q(x) = bnxn + bn-2xn-2 + … + b1x1 + b0 meaning that the shift has caused the new polynomial to lose its x^(n-1) term.

I know it has something to do with the significance of the 2nd coefficient polynomial, but I get lost after that. any help appreciated.