Question

f(x) = x⁴ − 3x² + 4, g(x) = x − 2

Answer 1

Let us denote the given polynomials as

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

`g(x) = x-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(2) = (2)^4 - 3 (2)^2 + 4`

        ` = 16 - 12 + 4`

        ` = 8`

We will calculate remainder by actual division

So the remainder is 8