Q. 65.0( 2 Votes )

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not:

f(x) = 2x3-9x2+x+12, g(x) = 3-2x

Answer :

We have,

f(x) = 2x3-9x2+x+12 and g(x) = 3-2x


In order to find g (x) = 3 – 2x = 2 (x - ) is a factor of f (x) or not, it is sufficient to prove that f () = 0


Now,


f(x) = 2x3-9x2+x+12


f () = 2 ()3 – 9 ()2 + + 12


= - + + 12


=


= 0


Hence, g (x) is a factor of f (x).


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