Question

what is meant by remainder theorem

Answer 1

Here's your answer..

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).

hope this helps..

Answer 2

Hey mate, here is your answer -:)

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The Factor Theorem states that if f(a)=0 for a polynomial then (x-a) is a factor of the polynomial f(x).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


HOPE it helps to you!!