"x-a is a factor of f(x) if and only if f(a)=0"......?

Question

What is the sufficient and what is the necessary condition of the factor theorem?

i did this wrong on a test. the ans is NOT x-a is a factor of f(x) is the sufficient condition. and f(a)=0 is the necessary condition.

i want to know what is the sufficient and what is the necessary condition of this statement.

loi.. thanks for ur ans but it is talking about polynomials

Answer 1

well, ti si true, if f(x) is a polynomial,
or a rational function,
but if f(x) is not a polynomial, then it is false:
example:
f(x)=2^x-1
then f(0)=2^0-1=0,
but in no way is x-0=x a factor of f(x)

another example:
f(x)=sin(x)
then f(2Pi)=sin( 2Pi)=0
but (x-2PI) is not a factor of sin(x)

Answer 2

The above condition is not true for all cases. The above condition is necessary and sufficient condition only if f(x) is a polynomial of any degree,

Answer 3

as lolitabelle said, it is valid for only polynomials... she is correct about necessary & sufficient conditions for (x-a) to be a factor of f(x)