What we are going to explore throughout this lesson is how to find all other zeros of a polynomial function given one zero.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
In other words, we are going to set the stage for how to find all rational zeros.
We will begin our lesson with understanding some important Theorems and what they mean in easy to understand terms:
- Remainder Theorem
- Factor Theorem
- Rational Zeros Theorem
Remember, zeros are just another way of saying roots or x-intercepts, and they are important to find so we can also graph polynomials and analyze their rate of change and end behavior.
Zeros of a Polynomial Function
Another way of thinking about it, as Purple Math states, is to say, “what values can I plug into the function so that I get an answer of zero?”
Then we will put everything into action by listing all possible zeros (roots) for a polynomial and also find all other zeros if we are provided with one root already.
We are also going to investigate the Conjugate Zeros Theorem, which is how we handle imaginary or complex roots.
Furthermore, we are also going to be able to work backward and write a polynomial function that satisfies given conditions!
Zeros Theorems Explained – Video
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