Question

state and prove the remainder theorem

Answer 1

Consider that a polynomial

P(x)

after division results in

where D is the divisor, Q is the quotient, and R is the remainder.

In this case, the polynomial is divided by

x-k

where k is a constant. This is the divisor, so

D(x) = x-k

.

Substituting the divisor into the polynomial, we have:

From here, you can easily see that

P(k) = R

:

Why x^n – y^n is divisible by x-y

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