How to Determine the Zeros of a Polynomial

The video tutorial explains how to find all zeros of a polynomial by first identifying possible rational zeros using the P/Q method. It then demonstrates how to verify these zeros using synthetic division. The tutorial suggests using a graphing calculator to simplify the process and provides a manual method for those without access to one. Finally, it covers factorization to find all zeros, emphasizing the importance of showing work through synthetic division.

What is the first step in finding all possible rational zeros of a polynomial?

• List all possible P/Q values

• Solve the polynomial equation

• Graph the polynomial

• Use synthetic division directly

Why is it recommended to use a graphing calculator when finding zeros of a polynomial?

• It automatically factors the polynomial

• It provides exact solutions without any further verification

• It helps visualize the polynomial and identify potential zeros

• It eliminates the need for synthetic division

If a graphing calculator is unavailable, what method should be used to find zeros?

• Use the quadratic formula

• Factor the polynomial directly

• Perform synthetic division with trial and error

• Use long division

In the example provided, what is the significance of obtaining a remainder of zero in synthetic division?

• It confirms that the divisor is a factor of the polynomial

• It means the polynomial is irreducible

• It indicates a calculation error

• It suggests the need for further division

After confirming a zero using synthetic division, what is the next step to find all zeros?

• Factor the remaining polynomial

• Graph the remaining polynomial

• Perform synthetic division again

• Use the quadratic formula on the remaining polynomial