Mathematica default display of polynomial is reverse the traditional form:
poly = x^3 + a*x + b*x^2 + c + d Out[251]= 27 + 3*a + 9*b + c + d
use Traditional Form with ParameterVariables to make it appear as in text books
TraditionalForm[poly, ParameterVariables :> {a, b, c, d}]