Question

which theorem is special case of remainder theorem.​

Answer 1

Step-by-step explanation:

Remainder Theorem

The theorem states that, if a polynomial f(x) is divided by x-b, then the remainder is the value of f(x), at x = b i.e., Remainder = f(b).

Statement:

On dividing a polynomial f(x) by x-b, the remainder will be f(b).

Proof:

Let p(x) be a polynomial divided by (x-b).

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

By division algorithm,

Dividend = (Divisor x quotient) + Remainder

p(x) = q(x) . (x-b) + R

Substitute x = b,

p(b) = q(b) (b-b) + R

p(b) = R (b - b = 0, 0 - q (b) = 0)

Hence Remainder = p(b)

Answer 2

Factor theorem may be the special case of remainder theorem.