Question

find the value of p for which (x-4) is a factor of :
$2x {}^{3} - 3x ^{2} - 3x {}^{2} = 18x + p$

Answer 1

given :-

p(x) = 2x³ - 3x² - 3x² = 18x + p

= 2x³ - 6x² = 18x + p

= 2x³ - 6x² - 18x - p = 0

g(x) = x - 4

therefore x = 4

on putting values :-

==> p(4) = 2(4)³ - 6(4)² - 18(4) - p = 0

==> 128 - 96 - 72 - p = 0

==> -40 - p = 0

==> -p = 40

==> p = -40

HOPE THIS HELPS..!!