Question

f(x) = x³ − 6x² + 2x − 4, g(x) = 1 − 2x

Answer 1

Let us denote the given polynomials as

         `f(x) = x^3 - 6x^2 + 2x - 4`

         `g(x) = 1-2x`

  `⇒ g(x) = -2 (x - 1/2)`

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(1/2) = (1/2)^3 -6 (1/2)^2 + 2(1/2) - 4`

            ` = 1/8 - 6 xx 1/4 + 2 xx 1/2 - 4`

           ` = 1/8 - 3/2 + 1 - 4`

           ` = 1/8 - 3/2 - 3`

            `= - 35/8`

Now we will calculate remainder by actual division

So the remainder is `(-35)/8`.