Question

6. State and prove 'Remainder theorai​

Answer 1

Answer:

If f(x) is divided by the linear polynomial (x-a) then the remainder is f(a). Remainder Theorem Proof: Let f(x) be any polynomial with degree greater than or equal to 1. Further suppose that when f(x) is divided by a linear polynomial p(x) = ( x -a), the quotient is q(x) and the remainder is r(x).

Answer 2

State:

The Remainder Theorem says that when a polynomial of degree f ( p ) is split by a binomial of degree p - x, the remainder of the end result is f. ( p ).

When we divide a polynomial $P(x)$

by $(x-c)$ the remainder equals $P(c)$

Prove :

$P(x) =(x-c) * Q(x) = R$

$P(c) = (c-c)*Q(c) + R$

$P(c) = 0*Q(c) + R$

$P(c) = R$