Question

what is the relation between the remainder and the value of the polynomial at x=r when the polynomial P(x) is divided by a binomial of the form x-r??

Answer 1

The relationship is that the remainder is the value of P(x) at x = r. That is P(r)

Explanation:

By the remainder theorem which states that if a linear factor x - a divides a polynomial P(x), then the remainder is the value of P(x) at x = a, that is P(a).

So for our question, when P(x) is divided by x - r, the remainder is obtained when x = r i inserted into P(x), that is P(r) which is the value of P(x) at x = r.

So, the remainder when P(x) is divided by x - r is the value of P(x) at x = r, that is P(r).