❖ Finding all the Zeros of a Polynomial - – Step-by-Step Example Using Rational Roots Test ❖

Finding All the Zeros of a Polynomial

In this video, I walk through how to find all the zeros of a polynomial of degree 4. Using the rational roots test, we determine all possible rational roots of the polynomial and test them until we find an actual root. From there, we use synthetic division to factor the polynomial step-by-step.

Step 1: Apply the rational roots test to find potential rational solutions.

Step 2: After finding a valid root, use synthetic division to factor the polynomial.

Step 3: Repeat the process on the remaining factor, reducing the polynomial degree each time.

Step 4: Once reduced to a quadratic, factor it by trial and error, fully factoring the original polynomial. Note that you can use any method you prefer but I use trial and error in this example.

Step 5: Set each factor equal to zero and find all the zeros of the polynomial.

This process may seem long, but by following it carefully, you’ll be able to fully factor any polynomial and find all its roots!

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