Question

Let us show that if n be any positive even integer, then x + y will be a factor of the polynomial
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NO WRONG ANSWER ,WRONG ANSWER WILL BE REPORTED!​

Answer 1

Step by step explanation:

Let us suppose, if ${x}^{n} - {y}^{n}$ is divided by x+y, the quotient is Q and

remainder without x is R.

$Dividend = Divisor \times Quotient + Remainder$

${x}^{n} - {y}^{n}$=(x+y) × Q+R [This is an identity]

Since x does not belong to the remainder R, the value of R will not change for any

value of x. So, in the above identity, putting (-y) for x, we get.

${-y}^{n} - {y}^{n}$=(-y+y) × Q+R

${x}^{n} - {y}^{n}$=0 × Q+R (°•° n is positive integer)

•°• R=0

•°• (x+y) is a factor of the polynomial ${x}^{n} - {y}^{n}$, when n is any positive

even integer.