 # Finding Zeros of a Polynomial Function

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Videos, worksheets, solutions, and activities to help PreCalculus students learn how to find the zeros or roots of a polynomial function.

The following figure show how to find the zeros or roots of a polynomial function. Scroll down the page for more examples and solutions. Finding Zeros of a Polynomial Function:
Finding the polynomial function zeros is not quite so straightforward when the polynomial is expanded and of a degree greater than two. One method is to use synthetic division, with which we can test possible polynomial function zeros found with the rational roots theorem. Once we find a zero we can partially factor the polynomial and then find the polynomial function zeros of a reduced polynomial.

How we find the zeros of a polynomial function in expanded form?
Finding all the Zeros of a Polynomial - Example 1.
This video shows how to find the remaining zeros of a polynomial given a few known zeros.
Example:
Given that one zero is x = 2 and another zero is x = 3, find the zeros and their multiplicities; let
f(x) = x4 - 10x3 + 37x2 - 60x + 36 Finding all the Zeros of a Polynomial - Example 2.
This video uses the rational roots test to find all possible rational roots; after finding one we can use long division to factor, and then repeat.
Example:
Find all the real zeros of the function:
f(x) = x3 + x2 - 10x + 8 Finding all the Zeros of a Polynomial - Example 3.
This video uses the rational roots test to find all possible rational roots; after finding one we can use long division to factor, and then repeat.
Example:
Find all the real zeros of the function:
f(x) = 3x4 - 8x3 - 37x2 + 2x + 40

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