Question

Give a proof for the remainder theorem

Answer 1

Remainder Theorem Proof
On dividing a polynomial F(x) by x - a, the remainder will be F(a).

Proof:

Let F(x) be a polynomial divided by (x - a).

Let Q(x) be the quotient and R be the remainder.

By division algorithm,

F(x) = Q(x)(x - a) + R .......................(i)

[Dividend = (Divisor x quotient) + Remainder]

Substituting x = a in equation (i), we have

F(a) = Q(a)(a - a) + R

⇒ F(a) = R

Hence, the remainder is F(a)