Question

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

Answer 1

It is given that f(x) = 2x³ − 9x² + x + 12 and g(x) = (3 − 2x)

By factor theorem, (3 − 2x) is the factor of f(x), if f(3/2)= 0

Therefore,

In order to prove that (3 − 2x) is a factor of f(x). It is sufficient to show that  `f(3/2) = 0`

Now,

`f(3/2) = 2(3/2)^3 -9(3/2)^2  +(3/2) + 12`

` = 27/4 - 81/4 + 3/2 + 12`

` = 54 / 4 + 3/2 + 12`

` = -27/2 + 3/2 +12`

` = -12 + 12`

`= 0`

Hence, (3 − 2x), is the factor of polynomial f(x).