Linear and polynomial regression practice

While practicing linear regression on kaggle,I implemented the math like it was shown in optional labs, however while checking other codes for the same dataset I saw that most of them utilized linear regression object. So is that how I have to do after sufficient practice?
Also if the dataset is non linear how am i suppose to figure out which polynomial terms i have to make and assign a weight?

The use of polynomial terms is covered later in the course.

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