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