# Polynomial Regression Intuition

I am taking following Andrew Ng's machine learning course and have just gotten to the polynomial regression. I have a hard time understanding the intuition of how it works and how the model equation is formulated mathematically. I was wondering if anyone can provide me with better clarity on this subject.

In addition to this, in his example and many other examples I have seen online, only use uni-variate$$(x_1)$$ polynomial regression. Is it possible to use multiple features $$(x_1, x_2, x_3, ...)$$ when using polynomial regression? If so how would it be done? Is it also possible that one feature has a linear relationship while another does not?