Question

f(x) = 3x³ + x² − 20x +12, g(x) = 3x − 2

Answer 1

It is given that `f(x) = 3x^3 + x^3 - 20x + 12` and  g(x) = 3x − 2

By the factor theorem,

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

Therefore,

In order to prove that (3x − 2) is a factor of f(x).

It is sufficient to show that  `f(2/3) =0.`

Now,

 `f(2/3) = 3(2/3)^3 +  (2/3) ^2 - 20(2/3) +12`

`= 3(8/27) + 4/9 - 40/3 + 12`

` = 8/9 + 4/9 - 40 /3 + 12`

` = 12/9 - 4/3`

` = 4/3 - 4/3`

`= 0`

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