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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)

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....!