Answer:
(x - 2) is not a factor of Q(x)
Explanation:
if (x - h) is a factor pf f(x) then f(h) = 0
if (x - 2) is a factor of Q(x) then Q(2) = 0
Q(2) = 2² - 3(2)² - 4(2) + 12
= 4 - 3(4) - 8 + 12
= 4 - 12 + 4
= - 8 + 4
= - 4
since Q(2) ≠ 0 then (x - 2) is not a factor of Q(x)
However , if the polynomial was meant to be
Q(x) = x³ - 3x² - 4x + 12 , then
Q(2) = 2³ - 3(2)² - 4(2) + 12
= 8 - 12 - 8 + 12
= 0
then (x - 2) is a factor of Q(x) = x³ - 3x² - 4x + 12