# 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

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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