Question

f(x) = 9x³ − 3x² + x − 5, g(x) = \[x - \frac{2}{3}\]

Answer 1

Let us denote the given polynomials as

`f(x) = 9x^2 - 3x^2 + x -5`

`g(x) = x2/3`

We have to find the remainder when f(x) is divided by g(x).

By the remainder theorem, when f(x) is divided by g(x) the remainder is

`f(2/3) = 9(2/3)^2 - 3 (2/3)^2 + (2/3) - 5`

             `= 9 xx 8 /27 - 3 xx 4/9 + 2/3 - 5`

              ` = 8/3 - 4/3 + 2/3 - 5`

               `= -3`

Remainder by actual division

Remainder is −3