Question

What is factor theorem explain with examples

Answer 1

Eg
f(x)=----------
P(x)=---------
Given p(x) is a factor of f(x)
Which means when both the polynomial are divided by each other gives the remainder as zero.
To find the remainder u should do it as the remainder 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