Question

Based on the polynomial remainder theorem, what is the value of the function when x=−6 ?

Answer 1

ANSWER

$f( - 6) = 10$


EXPLANATION

The given function is
$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$

According to the remainder theorem,

$f( - 6) = R$
where R is the remainder when
$f(x)$

is divided by
$x + 6$


We therefore substitute the value of x and evaluate to obtain,

$f( - 6) = { (- 6)}^{4} + 8 {( - 6)}^{3} + 10 { (- 6)}^{2} - 7( - 6)+ 40$




$f( - 6) = 1296 + 8 ( - 216) + 10 (36) - 7( - 6)+ 40$




$f( - 6) = 1296 - 1728 + 360 + 42+ 40$



This will evaluate to,


$f( - 6) = 10$


Hence the value of the function when
$x = - 6$

is
$10$



According to the remainder theorem,
$10$
is the remainder when

$f(x) = {x}^{4} + 8 {x}^{3} + 10 {x}^{2} - 7x + 40$
is divided by
$x + 6$