factoring polynomials with degree greater than

Question

Factoring Polynomials with Degree Greater than 2

There is no one method for doing these generally.  However, there are some that we can do so

let's take a look at a some examples.

Example : Factor each of the following.

                 A)3x⁴ - 3x³ - 36x²

                  B)     X⁴-25  

Solution

A)3x⁴ - 3x³ - 36x²

In this question let's notice that we can factor a common factor of 3x2 from all of the terms thus let's do that first.

3x⁴ - 3x³ - 36x²  = 3x² ( x² - x -12)

What is left is a quadratic which we can employ the techniques from above to factor.  Doing this gives us,

3x⁴ - 3x³ - 36x²  = 3x² + x - 4= (x + 3)

Don't forget that the FIRST step to factoring must always be to factor out the greatest common factor. It can only help the procedure.