Solving Higher Degree Polynomials by Synthetic Division and the Rational Roots Test

The video tutorial introduces synthetic division as a method to test if a polynomial is divisible by a particular expression. It explains the process through examples, demonstrating how to find factors and solutions of polynomials. The tutorial also covers the rational roots test, which helps identify potential solutions for higher-degree polynomials. By the end, viewers learn how to apply synthetic division and the rational roots test to solve complex polynomial equations.

How can you determine if a polynomial is prime or can be factored?

Explain the process of testing if a polynomial is divisible by a particular expression using synthetic division.

What is synthetic division and how does it relate to long division?

What does it mean if the remainder is zero in synthetic division?

What are the steps to factor a polynomial after finding a solution using synthetic division?

What are the four solutions found for the quartic equation discussed in the text?

Describe how to use the rational roots test to find possible solutions for a polynomial.