Lecture-2 (Class-9th|10th) #Polynomial_Series -- Factor , Remainder theoram & depressed polynomial

Mathematics #Polynomial-Series-Part_2
The Remainder Theorem
When we divide f(x) by the simple polynomial x−c we get:

f(x) = (x−c)·q(x) + r(x)
x−c is degree 1, so r(x) must have degree 0, so it is just some constant r :
f(x) = (x−c)·q(x) + r
Now see what happens when we have x equal to c:
f(c) =(c−c)·q(c) + r
f(c) =(0)·q(c) + r
f(c) =r
The Factor Theorem
Now ...
What if we calculate f(c) and it is 0?
... that means the remainder is 0, and ...
... (x−c) must be a factor of the polynomial!
And so we have:
The Factor Theorem:
When f(c)=0 then x−c is a factor of f(x)
And the other way around, too:
When x−c is a factor of f(x) then f(c)=0

polynomial