Polynomials Rational Root Theorem

This section has the following videos:

  • Lesson Video
  • Example Set A Practice Problems (Video Solutions)
  • Example Set B Practice Problems (Video Solutions)
  • Example Set C Practice Problems (Video Solutions)
  • Example Set D Practice Problems (Video Solutions)

In this lesson I will teach you the rational root theorem.  The theorem is also known as the rational-zero test and it’s purpose is extremely important in our effort to solve polynomial equations.  Before I get into an explanation of the rational root theorem make sure you totally understand polynomial division and the remainder/factor theorem.  Ok what is the rational root theorem?  Well basically it’s a  theorem that gives us all the “possible” rational roots/solutions a polynomial may contain.  Recall that rational numbers are those numbers that can be expressed as fractions where the numerator and denominator are integers.  Examples of rational numbers would be -3, 4/9, 0, 6, -1/3, etc.  The theorem gives us a way to list all possible rational roots a polynomial may have.  The key thing I want you to focus on is the list is all POSSIBLE SOLUTIONS so we need to check to see if in fact any numbers in the list are actual solutions.  The best way for us to check is using the remainder theorem- lots more about this in the lesson.  So as you get ready to watch the full lesson remember that the rational root theorem is another “tool” that we are learning to solve polynomial equations.  Good luck and stay motivated!