Linear regression vs Polynomial regression?

Suppose we have a dataset with multiple columns and we see a linear relation with some columns and with other columns we don't see a linear relation plus we have categorial columns too.

Does it make sense to fit a Polynomial regression for this instead of a linear regression? Or is the general process trying both and seeing which performs better?


But just by intuition, I feel that a polynomial regression would perform better.

datascience dataset general linear linear regression multiple polynomial process regression sense