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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
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.
Find all the eighth roots of (19 + 7 i)
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