Question

Decide using factor theorem whether (x-2) is a factor of x³-4x²-4

Answer 1

x = 2

(2)^3 - 4(2)^2 -4
8 - 16 - 4
8-20
-12

Answer 2

let
p(x)=x³-4x²-4,
(x-2) will be a factor of p(x) if
p(2)=0,

then
p(2)=2³-4(2)²-4,

p(2)=8-4×4-4,

p(2)=8-16-4,

p(2)=-12,

since
p(2) not equal to zero then (x-2) is not a factor of p(x)