Question

In each of the following, use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x) or, not: (1−7) 

f(x) = x³ − 6x² + 11x − 6; g(x) = x − 3

Answer 1

Given that:  `f(x) = x^3 - x^3 - 6x^2 + 11x - 6,`

 `g(x)= x- 3,`

By the factor theorem,

If g(x) is a factor of f(x)

i.e.  x - 3 =0

⇒ x = 3

Then

`f(3) = (3)^3 + 6(3)^2 + 11(3) - 6`

          ` = 27 - 54 + 33 - 6`

          ` = 60 - 60`

          ` = 0`

As f(3) is zero therefore g(x), is the factor of polynomial f(x).