Synthetic division and polynomial long division are super helpful tools for finding the roots of polynomial functions. This is especially true when you are working with polynomials that have a high degree.

Synthetic Division:

• This method is a faster way to divide polynomials, especially when you want to check possible roots using the Rational Root Theorem.
• You create a simple table that helps you quickly find the remainder.
• If the remainder is zero, congratulations! You’ve found a root, and you can factor it out!

Polynomial Long Division:

• This method is the traditional way of dividing polynomials.
• It works better when a polynomial is not suitable for synthetic division.
• You will break down the polynomial step by step, which helps you find the quotient and the remainder.

Both of these methods help you lower a polynomial’s degree, which makes it easier to find more roots. Overall, they simplify your work and help you get to the answers faster.