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

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

  • Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

      • What's a Rational Number?What's a Rational Number?

      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!

  • Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

      • What's an Irrational Number?What's an Irrational Number?

      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.

  • Interpret parts of an expression, such as terms, factors, and coefficients.

      • What's a Factor?What's a 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!

  • Factor a quadratic expression to reveal the zeros of the function it defines.

      • How Do You Solve a Quadratic Equation by Factoring?How Do You Solve a Quadratic Equation by Factoring?

      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!

  • Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).

      • What is the Factor Theorem?What is 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.

  • Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.