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)3x^{4} - 3x^{3 }- 36x^{2}
B) X^{4}-25
Solution
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.
3x^{4} - 3x^{3} - 36x^{2} = 3x^{2} ( x^{2} - x -12)
What is left is a quadratic which we can employ the techniques from above to factor. Doing this gives us,
3x^{4} - 3x^{3} - 36x^{2 } = 3x^{2} + 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.