Question

What is factor theorem and what is remainder theorem? Explain with examples.

Answer 1

when f(x) is divided by (x-a),then remainder is f(a) ,this is remainder theorem.
If f(a)=0,then (x-a)is a factor of f(x).
This is called factor theorem .

Answer 2

☛ Factor Theorem ;

If p ( x ) is a polynomial of degree ≥ one and a is any real number , then

( i ) ( x - a ) is a factor of p ( x ) , if p ( a ) = 0.

( ii ) p ( a ) = 0, if ( x - a ) is a factor of p (x).


☛ Remainder Theorem ;

Division and Algorithm for polynomials : If p(x) and g(x) are two polynomials with g(x) ≠ 0, then we can find q ( x ) and r (x) and such that

p ( x ) = g ( x ) * q ( x ) + r ( x ), where
r (x) = 0 (or) deg r(x) < deg g(x)

Dividend = Divisor × quotient + remainder