Question

| Theorems :
Remainder theorm :
If p (x) be a polynomial of degree n greater than 1. and let a be any real number. when p (X) is
divided by x - a, then the remainder is p (a).​

Answer 1

Answer:

Remainder = P(a)

Step-by-step explanation:

Remainder theorm :

If p (x) be a polynomial of degree n greater than 1. and let a be any real number. when p (X) is

divided by x - a, then the remainder is p (a).​

Yes Theorem is correct

Let p(x) be any polynomial of degree greater than or equal to 1.

p(x) is divided by x-a (where a is a divisor),

the quotient is q(x) and

the remainder is r

Dividend = (Divisor x quotient) + Remainder

p(x) = (x-a) q(x) + r

Since the degree of x-a is less than the p(x) and the degree of r(x) is less than the degree of x-a,

p(a) = (a -a)q(x) + r

=> P(a) = 0 * q(x) + r

=> P(a) = r

Hence remainder = P(a)