Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#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 bundy
Administrator
Registered: 2010-06-20
Posts: 8,399

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


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

Offline

Board footer

Powered by FluxBB