There are a few similar Questions, including a couple with Accepted but broad brush Answers. For example, [Why does dividing a polynomial by x−a give the same quotient as evaluating it at x=a using synthetic division?](https://math.stackexchange.com/questions/2928272/why-does-dividing-a-polynomial-by-x-a-give-the-same-quotient-as-evaluating-it)