Answer 1

Let us denote the given polynomials as

`f(x) = 4x^2 - 12x^3 - 12x^2 + 14x - 3,`

`g(x) = 2x - 1`

`⇒ 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) = 4(1/2)^3 - 12(1/2)^2 + 14 (1/2) - 3`

            ` = 4 xx 1/8 - 12  xx 1/4 + 14 xx 1/2 - 3`

            `  = 1/2 -3 + 7 - 3`

             `= 3/2`

Now we will calculate the remainder by actual division

So the remainder by actual division is `3/2` .