Question

Sharon is absent in your class today and yesterday and she needed help on how to find the zeros of a higher-degree polynomial function.

Explain each step in the process

Answer 1

To find the zeros of a higher-degree polynomial, identify the polynomial function, factor it if possible, solve for the zeros, use numerical methods or software for complex cases, and verify the potential zeros by plugging them back into the original equation.

Step-by-step explanation:

To find the zeros of a higher-degree polynomial function, Sharon should follow these steps:

1. Identify the polynomial function that she is working with. This is her unknown. The zeros are the values of x that make the polynomial equal to zero.
2. Next, factor the polynomial if possible. Factoring breaks down the polynomial into simpler terms that can be set to zero.
3. Solve for the zeros by setting each factor that contains a variable equal to zero and solving for the variable.
4. In cases where the polynomial cannot easily be factored, use methods such as synthetic division or the Rational Root Theorem to find potential zeros, or graph the function to estimate the zeros.
5. For polynomials that don't have rational zeros or cannot be factored, use numerical methods like Newton's method or software that can find approximate zeros.
6. Verify the potential zeros by plugging them back into the original polynomial equation to ensure that they indeed give a zero value.

Each step should be carried out carefully to ensure an accurate solution. Tackling the problem methodically by breaking it into parts — first finding and working with the knowns, then solving for the unknowns — will lead to success.