Unformatted text preview: ut none of those special
cases will be seen here.
Factoring Polynomials with Degree Greater than 2
There is no one method for doing these in general. However, there are some that we can do so
let’s take a look at a couple of examples. Example 5 Factor each of the following.
(a) 3 x 4 - 3 x 3 - 36 x 2 [Solution]
(b) x 4 - 25 [Solution]
(c) x 4 + x 2 - 20 [Solution]
(a) 3 x 4 - 3 x 3 - 36 x 2
In this case let’s notice that we can factor out a common factor of 3x2 from all the terms so let’s
do that first. 3 x 4 - 3x3 - 36 x 2 = 3x 2 ( x 2 - x - 12 ) What is left is a quadratic that we can use the techniques from above to factor. Doing this gives
us, 3x 4 - 3x3 - 36 x 2 = 3x 2 ( x - 4 ) ( x + 3) Don’t forget that the FIRST step to factoring should always be to factor out the greatest common
factor. This can only help the process.
[Return to Problems] (b) x 4 - 25
There is no greatest common factor here. However, notice that this is the difference of two
perfect squares. x 4 - 25 = ( x 2 ) - ( 5...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12