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More Lessons for PreCalculus

Math Worksheets

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) = x^{4} - 10x^{3} + 37x^{2} - 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) = x^{3} + x^{2} - 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) = 3x^{4} - 8x^{3} - 37x^{2} + 2x + 40

More Lessons for PreCalculus

Math Worksheets

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 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.

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) = x

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) = x

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) = 3x

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