Question

what is factor theorem

Answer 1

the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. 
f(x)=2x-6
x=3
which is 2*3-6=0

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