Question

find whether x^n+y^n is divisible by x-y ( y not equal to 0) or not​

Answer 1

xⁿ + yⁿ is not divisible by x - y  if y ≠ 0

Given:

• Expression xⁿ + yⁿ
• y ≠ 0

To Find:

• xⁿ + yⁿ is divisible by x - y or not

Solution:

Factor Theorem:

x – a is a factor of the polynomial p(x), if p(a) = 0.  

Also, if x – a is a factor of p(x), then p(a) = 0,

Step 1:

Assume P(x) = xⁿ + yⁿ

Step 2:

Considering x - y as factor  substitute x= y

P(y) = yⁿ + yⁿ

P(y) = 2yⁿ

as y ≠ 0 Hence

P(y) ≠ 0

As P(y) ≠ 0 hence x - y is not a factor

Hence xⁿ + yⁿ is not divisible by x - y

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