SOLUTION: Simplify: (x^5 + y^5)/(x + y) After spending much time beating on this problem as a long division with my 8th grader it dawned on me that perhaps the equation is already simpli

Question 38196: Simplify:
(x^5 + y^5)/(x + y)
After spending much time beating on this problem as a long division with my 8th grader it dawned on me that perhaps the equation is already simplified. An online equation calculator seems to confirm that fact.
My question: is there an easy check or a simple trick that would quickly confirm that this equation (or a similar equation) is already in its simplest form?
Thanks,
Robert
Found 2 solutions by stanbon, askmemath:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(x^5 + y^5)/(x + y)
It does divide.
The quotient is x^4-x^3y+x^2y^2-xy^3+y^4
Check MATHWORLD polynomial division using Google on your other question.
Cheers,
Stan H.

Answer by askmemath(368) (Show Source): You can put this solution on YOUR website!
Some Rules that might help you

1.NEVER divisible by a-b
2.n is Odd Divisible by a+b
n is Even NOT Divisible

1.ALWAYS divisible by a-b
2.n is Even DIVISIBLE by a+b
n is Odd NOT Divisible by a+b
RELATED QUESTIONS
Hello, My 8th grader is stuck on problems involving systems of equations and inequality, (answered by stanbon)
Though this question is not out of our textook, it is based on Chapter 6. We are studying (answered by edjones)
I need to create a word problem and I am having a hard time setting up the problem once I (answered by josmiceli)
Hello my name is Aaliyah and I really need help on this problem. 2x-5y=-158 x-y=-40... (answered by nerdybill,feliz1965,stanbon)
Solve using long division, then CHECK. (-30+6y^3-28y+y^2) divided by (2y-5)... (answered by ankor@dixie-net.com)
I'm having problems with this problem, I can not get it to come out. Divide by long... (answered by Fombitz)
trying to help my 7th grader , with his 8th grerade pre algebra. He knows the basis of... (answered by Alan3354)
am trying to help my 9th grader with algebra....the problem is:... (answered by nerdybill,Earlsdon,stanbon)
Good afternoon, I need some help with this problem please. I been stuck on it for a week... (answered by ankor@dixie-net.com)