Remainder and Factor Theorem

In this lesson I will teach you about the remainder and factor theorem.  These theorems will require your ability to do polynomial division so please review that lesson if your unsure about your polynomial division skill level.  The remainder theorem is a cool way (at least I think it’s cool) to evaluate functions.  For example if I told you to evaluate the function f(x) =3x + 10 for x =5  you would plug in the value 5 for x in the following manner and simplify-  f(5)=3(5) + 10.  As you can see the value of f(5) = 25.  Now this is a pretty simple function so it’s easy just to evaluate it in the manner I just did.  However there is another totally different way we can evaluate a function using polynomial division.  What we do is use synthetic division and look at the value of the remainder- this will tell us the same value as evaluating a function.  Confused?  Don’t worry I will explain this much more clearly in the lesson.  The other theorem we will learn is called the factor theorem.  It also uses polynomial division but it’s purpose is to identify linear factors in polynomials.  We are covering these detailed concepts about of polynomials because we need all these skills to solve advance polynomial equations.  Remember to take your time and practice is a must!