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#1 2018-05-27 18:05:25
- Doggone
- Guest
Algebra
Determine a constant k such that the polynomial
P(x, y, z) = x^5 + y^5 + z^5 + k(x^3+y^3+z^3)(x^2+y^2+z^2)
is divisible by x+y+z.
Thanks in advance!
#2 2018-05-28 00:45:12
- Bob
- Administrator
- Registered: 2010-06-20
- Posts: 10,640
Re: Algebra
hi Doggone
Welcome to the forum.
So
That has to be true for all values of x, y and z, so I chose a set of values that makes life easy:
If x = y = 1 and z = -2, then x + y + z = 0 and the equation becomes
From here you can get k.
Bob
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You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you! …………….Bob 
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