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**Doggone****Guest**

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!

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,442

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

Children are not defined by school ...........The Fonz

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 Bundy

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