Question

find the value of k for which (x-4) is a factor of 2 xcube - 3xsquare -18x + k

Answer 1

Given expression
$2 {x}^{3} - 3 {x}^{2} - 18x + k$


And we have (x-4) as a factor, so ine of the zero/root of that equation would be x -4= 0
x = 4


By using factor theorem,

$p(x) = 2 {x}^{3} - 3 {x}^{2} - 18x + k$
Substitute for x
$p(4) = 2{(4)}^{3} - 3 {(4)}^{2} - 18(4) + k = 0 \\ 128 - 48 - 72 + k = 0 \\ 128 - 120 + k = 0 \\ 8 + k = 0 \\ k = - 8$


Thereofe k must be equal to -8 in order to have a factor as (x-4)

Answer 2

Hope it will be help you