Question

f(x) = 2x⁴ − 6x³ + 2x² − x + 2, g(x) = x + 2

Answer 1

Let us denote the given polynomials as

        `f(x) = 2x^4 -6x^3 + 2x^2 - x + 2`

       `g(x) = x+2`

`⇒ 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 (-2)^4 - 6(-2)^3 + 2(-2)^2 - (-2) + 2 `

` = 32 + 48 + 8 + 2 + 2`

` = 92`

Now we will calculate the remainder by actual division

So the remainder by actual division is 92.