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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   



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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
Some Rules that might help you
a%5En+%2B+b%5En
1.NEVER divisible by a-b
2.n is Odd Divisible by a+b
n is Even NOT Divisible
a%5En+-+b%5En
1.ALWAYS divisible by a-b
2.n is Even DIVISIBLE by a+b
n is Odd NOT Divisible by a+b