I need an explanation with the increase exponent function

For a few days I have been struggling understanding the algorithm. After going through a lot of videos and posts I have a basic understanding of the algorithm. But when it came to the implementation I just couldn’t get it right. I haven’t used the increase exponent function and I think that is the part of the code I am missing. So I would appreciate it if someone would explain to me what that functions job is.

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Let polynomial be A0. If I want to have the expression A0 * x^2, I will use increase_exponent(A0, 2) in my code. I am essentially increasing the degree of every component of A0 by 2. So in python, you just need to put in 2 additional zeros at the start of the list of A0.

I hope this resolve your confusion.