How Do You Find All the Rational Zeros of a Polynomial Function?

Note:

Polynomial functions with integer coefficients may have rational roots. The Rational Root Theorem lets you determine the possible candidates quickly and easily! Watch the video to learn more.

Keywords:

problem
zeros
roots
polynomial function
rational zeros
synthetic division

Background Tutorials

Rational Number Definitions
- What's a Rational Number?
  
  There are lots of different kind of numbers that you should know about, and that includes rational numbers. Check out the tutorial!
Factors and Greatest Common Factor
- What's a Factor?
  
  Factors are a fundamental part of algebra, so it would be a great idea to know all about them. This tutorial can help! Take a look!
Function Definitions and Notation
- How Do You Find f(x) If You Have a Value For x?
  
  To solve a function for a given value, plug that value into the function and simplify. See this first-hand by watching this tutorial!
Real Number Definitions
- What's an Irrational Number?
  
  Is an irrational number just a way to describe a number that's lost its mind? Not really. :) An irrational number is simply a number that cannot be written as a fraction. Check out the definition, learn an important property of these special numbers, and take a look at some examples of irrational numbers.
Degrees of Monomials and Polynomials
- How Do You Find the Degree of a Polynomial?
  
  Terms and polynomials can't run a fever, but they do have degrees! This tutorial will tell you all about the degree of a term and of a polynomial and will show you how to find it!
Working with Integers
- What's an Integer?
  
  There are lots of different kinds of numbers that you'll come across in algebra, and a lot of these kinds of numbers are related to each other. Before you learn how they are related, you've got to learn about them separately, and in this tutorial you'll how to define integers :)
From Factoring to Solving
- How Do You Solve a Quadratic Equation by Factoring?
  
  One of the many ways you can solve a quadratic equation is by factoring it. In this tutorial, you'll see how to factor a quadratic equation using the guess and check method of factoring. Then, use the zero product property to find the solution!
Simplifying Polynomial Expressions
- What is a Leading Coefficient?
  
  Where do you think a leading coefficient is located in a polynomial? The name gives a great hint! This tutorial introduces you to the leading coefficient of a polynomial and shows you exactly where it's located.
The Factor Theorem
- What is the Factor Theorem?
  
  Trying to figure out if a given binomial is a factor of a certain polynomial? This tutorial can help you find the answer! Follow along to learn about the Factor Theorem and how it can be used to find the factors and zeros of a polynomial.