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

$124$

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,

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

$f(4) = 124$