Question

f(x) = 4x⁴ − 3x³ − 2x² + x − 7, g(x) = x − 1

Answer 1

Let us denote the given polynomials as

`f (x) = 4x^4 - 3x^3 - 2x^2 + x - 7`

`g(x) = x-1`

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

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

`f(1) = 4(1)^4 - 3(1)^3 - 2(1)^2 + 1-7`

        ` = 4 - 3- 2 + 1- 7`

         ` = -7`

Now we will show remainder by actual division

So the remainder by actual division is −7