Determine which of the following polynomials has $(x-2)$ as a factor:
$A) 3x^2 + 6x - 24$
$B) 4x^2 + x - 2$

(A) We know that if $(x-a)$ is a factor of $p(x)$,then $p(a) = 0$.
$(i)$ Let $p(x) = 3x^2 + 6x - 24$.
If $(x-2)$ is a factor of $p(x)$,then $p(2)$ must be equal to $0$.
$p(2) = 3(2)^2 + 6(2) - 24 = 3(4) + 12 - 24 = 12 + 12 - 24 = 0$.
Since $p(2) = 0$,by the factor theorem,$(x-2)$ is a factor of $3x^2 + 6x - 24$.
$(ii)$ Let $p(x) = 4x^2 + x - 2$.
If $(x-2)$ is a factor of $p(x)$,then $p(2)$ must be equal to $0$.
$p(2) = 4(2)^2 + 2 - 2 = 4(4) + 0 = 16$.
Since $p(2) \neq 0$,$(x-2)$ is not a factor of $4x^2 + x - 2$.