m = -2
Explanation:The given function is:
[tex]f(x)=x^3+2mx^2+6x-4[/tex]For x - 2 to be a factor of f(x):
f(x) must be equal to zero when x = 2
[tex]\begin{gathered} f(2)=2^3+2m(2^2)+6(2)-4 \\ f(2)=8+8m+12-4 \\ f(2)=8m+16 \end{gathered}[/tex]Let f(2) = 0 to solve for m
8m + 16 = 0
8m = -16
m = -16/8
m = -2
Therefore, for x - 2 to be a factor of x^3 + 2mx^2 +6x -4, the value of m is -2
