Doesn’t polynomial regression violate the multicollinearity assumption for Linear Regression? 

While the original variable will likely be correlated with a higher order term constructed from the same variable, multicollinearity is not an overt cause of concern because the full effect of the variable consists of contributions from both the original and transformed component. In a model containing both X and X², the effect of the variable X is the composite of the first and second order terms. Thus, the assumption of multicollinearity in linear regression is restricted to the independent, first-order effects. However, the inherent correlation introduced by including a polynomial term can be addressed by centering the original variable (subtracting each value by the overall mean of the variable) and then performing the transformation on the centered representation.