Find zeros of a polynomial function

Learn how to find zeros of a polynomial function with a few well-chosen examples.

Example #1

Find the zeros of f(x) = (x - 4)(x + 2)(x + 5)

Using the zero product property, find a zero for each linear factor

x - 4 = 0

x - 4 + 4 = 0 + 4

x = 4

x + 2 = 0

x + 2 - 2 = 0 - 2

x = -2

x + 5 = 0

x + 5 - 5 = 0 - 5

x = -5

The zeros of the function f(x) = (x - 4)(x + 2)(x + 5) are 4, -2, and -5

Example #2

Find the zeros of f(x) = x4 - x2

We cannot use the zero product property yet since we cannot see the linear factors.

Rewrite the function f(x) = x4 - x2 to show its linear factors. We can do this by factoring the function completely.

f(x) = x4 - x2

f(x) = x2(x2 - 1)

f(x) = (x)(x)(x - 1)(x + 1)

Now you can use the zero product property to find the zero for each linear factor.

x = 0

x = 0

x - 1 = 0

x - 1 + 1 = 0 + 1

x = 1

x + 1 = 0

x + 1 - 1 = 0 - 1

x = -1

The zeros of the function f(x) = x4 - xare 0, 1, and -1

Example #3

Find the zeros of f(x) = 8x3 - 8x2 - 160x

We cannot use the zero product property yet since we cannot see the linear factors.

Rewrite the function f(x) = 8x3 - 8x2 - 160x to show its linear factors. We can do this by factoring the function completely.

f(x) = 8x3 - 8x2 - 160x

f(x) = 8x(x2 - x - 20)

f(x) = 8x(x - 5)(x + 4)

Using the zero product property, find a zero for each linear factor

8x = 0

x = 0

x - 5 = 0

x - 5 + 5 = 0 + 5

x = 5

x + 4 = 0

x + 4 - 4 = 0 - 4

x = -4

The zeros of the function f(x) = 8x3 - 8x2 - 160x are 0, 5, and -4

Recent Articles

  1. How To Find The Factors Of 20: A Simple Way

    Sep 17, 23 09:46 AM

    Positive factors of 20
    There are many ways to find the factors of 20. A simple way is to...

    Read More

  2. The SAT Math Test: How To Be Prepared To Face It And Survive

    Jun 09, 23 12:04 PM

    SAT math
    The SAT Math section is known for being difficult. But it doesn’t have to be. Learn how to be prepared and complete the section with confidence here.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes