Polynomial regression

Hello everybody,
I am completing a quizz in order to prepare an exam, and I have some doubts concerning a question:
I know the polynomial models can be adjusted by linear least squares regression since, although they generate nonlinear models, their equation is still a linear equation with predictors x, x2, x3, ..., xd. For this same reason, polynomial functions can be used in logistic regression to predict binary responses. It is only necessary to perform a logit transformation. However I am not at all sure about what exactly happens when we center predictors.
Thank you for your help!