How do you find the greatest common factors of variable expressions?
The 'normal' way of finding the GCF of two polynomials is to factor both of them completely, then pick out the common factors and multiply them together.
Alternatively you can use division.
Normal Method - Factor both polynomials first
you can factor
hence the GCF is
Backup Method - Using division of polynomials
If we now divide
Next try dividing
This time there is no remainder, so
For a more complex example, see http://socratic.org/questions/if-you-are-told-that-x-7-3x-5-x-4-4x-2-4x-4-0-has-at-least-one-repeated-root-how