Table of Contents

- 1 What do the zeros of a polynomial represent?
- 2 What are the zeros of the polynomial shown in the graph?
- 3 How do you write the zeros of a polynomial function?
- 4 How do you find the zeros of a function?
- 5 How do you find the zeros of a polynomial?
- 6 How do you find a polynomial function with given zeros?

## What do the zeros of a polynomial represent?

The zeros of a polynomial p(x) are all the x-values that make the polynomial equal to zero. They are interesting to us for many reasons, one of which is that they tell us about the x-intercepts of the polynomial’s graph. We will also see that they are directly related to the factors of the polynomial.

## What are the zeros of the polynomial shown in the graph?

The zeros of a polynomial are the solutions to the equation p(x) = 0, where p(x) represents the polynomial. If we graph this polynomial as y = p(x), then you can see that these are the values of x where y = 0. In other words, they are the x-intercepts of the graph.

**How are the zeros of polynomial function useful in graphing them?**

The graphical connection The multiplicity of a zero is important because it tells us how the graph of the polynomial will behave around the zero.

### How do you write the zeros of a polynomial function?

The zeros of a polynomial are the values of x which satisfy the equation y = f(x). Here f(x) is a function of x, and the zeros of the polynomial is the values of x for which the y value is equal to zero. The number of zeros of a polynomial depends on the degree of the equation y = f(x).

### How do you find the zeros of a function?

Use the Rational Zero Theorem to list all possible rational zeros of the function. Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial. If the remainder is 0, the candidate is a zero. If the remainder is not zero, discard the candidate.

**How many zeros does a polynomial function have?**

A polynomial function may have zero, one, or many zeros. All polynomial functions of positive, odd order have at least one zero, while polynomial functions of positive, even order may not have a zero. Regardless of odd or even, any polynomial of positive order can have a maximum number of zeros equal to its order.

## How do you find the zeros of a polynomial?

Find Zeros of a Polynomial Functions

- Use the Rational Zero Theorem to list all possible rational zeros of the function.
- Use synthetic division to evaluate a given possible zero by synthetically dividing the candidate into the polynomial.
- Repeat step two using the quotient found with synthetic division.

## How do you find a polynomial function with given zeros?

Step 1: Start with the factored form of a polynomial. Step 2: Insert the given zeros and simplify. Step 3: Multiply the factored terms together. Step 4: The answer can be left with the generic “ ”, or a value for “ ”can be chosen, inserted, and distributed.