SOLUTION: I am in the process of learning factorization of monomials. The Largest Common Factor is somewhat confusing for me. How do you find the correct LCF when there is an exponent? Ex

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Question 848214: I am in the process of learning factorization of monomials.
The Largest Common Factor is somewhat confusing for me. How do you find the correct LCF when there is an exponent?
Example:
24x^5y^2 + 18x^4y^6 - 30x^6y^4
I know that 6 would be the LCF, how do I know about the exponent?
Thanks!
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
By finding the GCF (or as you call it LCF) we isolate what is common in all of the terms.
Let's look at just the first two terms and break them down according to their prime factorization.


So we can see that 2*3*x*x*x*x*y*y is our LCF or 6*x^4*y^2 for the first two terms. We now try this with all 3.
24x^5y^2 + 18x^4y^6 - 30x^6y^4
What we did before was the long way, but I think it will help you see what is going on.
What is in common with 24,18,30? highlight%286%29. That's part of our factor.
What is in common with x^5, x^4, x^6? highlight%28x%5E4%29 [they all contain at least 4 xs.]
What is in common with y^2, y^6, y^4? highlight%28y%5E2%29 [they all contain at least 2 ys.]
So our final answer is highlight%286x%5E4y%5E2%29