Remainder Theorem : Let p(x) be any polynomial of degree greater than

1.	Remainder Theorem : Let p(x) be any polynomial of degree greater than orequal to one and let a be any real number. If p(x) is divided by the linearpoynomial x - a, then the remainder is p(a).
Answer» 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= (Divisorx quotient) + Remainder] Substituting x = a inequation(i), we have F(a) = Q(a)(a - a) + R ⇒⇒F(a) = R Hence, the remainder is F(a).

Remainder Theorem : Let p(x) be any polynomial of degree greater than orequal to one and let a be any real number. If p(x) is divided by the linearpoynomial x - a, then the remainder is p(a).

Answer»

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= (Divisorx quotient) + Remainder]

Substituting x = a inequation(i), we have

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

⇒⇒F(a) = R

Hence, the remainder is F(a).