Question

I DID NOT UNDERSTOOD THE FACTOR THEORUM

Answer 1

for any expressionf(x)
if f(a)=0
the (x−a) is factor of f(x)
for example consider
f(x) =x²−5x+ 6
f(2) =2²−5×2+ 6 =4−10+ 6 =0
that means x−2 is a factor of  x²−5x+ 6
and x²−5x+ 6 =(x−2)(x−3)

Answer 2

According to factor theorem,if s is factor of any polynomial P(x) i.e., if P(s) =0 then (x-s) is factor of the polynomial P(x).
EXAMPLE OF FACTOR THEOREM:
factors of 2 x^2-5x+3?
Step 1:let f(x)=2x^2-5x+3
Step 2:let us x=1 by trial and error method.then,f(1) =2(1)^2-5(1)+3 =0
Step 3:According to factor theorem,if f(1)=0 then (x-1) is a factor of the polynomial f(x).
Step 4:therefore,(x-1) is a factor of the given polynomial.
Step 5:by dividing the polynomial by (x-1),we get (2x-3).
Step 6:so,the factors of the given polynomial are (2x-3) and (x-1).
THIS IS CALLED FACTOR THEOREM....
if any doubts,ask me....!