Question

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)

f(x) = x³ + 4x² − 3x + 10, g(x) = x + 4

Answer 1

Let us denote the given polynomials as

           `f(x) = x^3 + 4x^2 - 3x + 10,`

          `g(x) = x+ 4`

  `⇒ g (x) = x - (-4)`

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(-4) = (-4)^3 +4(-4)^2 - 3(-4) + 10`

             ` = -64 + 64 + 12 + 10`

             `= 22`

Now we will show by actual division

So the remainder by actual division is 22