Question

Based on the polynomial remainder theorem, what is the value of the function when x = 4? f(x)=x4−2x3+5x2−20x−4

Answer 1

The answer is f(x) = 124

Answer 2

ANSWER

The remainder is


`124`

Step-by-step explanation

According to the remainder theorem, if


`f(x) = {x}^(4) - 2 {x}^(3) + 5 {x}^(2) - 20x - 4`

is divided by


`(x - 4)`

then the remainder is given by


`f(4)`

So we substitute

`x = 4`
into the given function to get,


`f(4) = {4}^(4) - 2 {(4)}^(3) + 5 {(4)}^(2) - 20(4) - 4`

We evaluate to get,


`f(4) = 256- 2 {(64)} + 5 {(16)} - 20(4) - 4`

This will simplify to,


`f(4) = 256- 128 + 80- 80 - 4`


`f(4) = 124`