if (x-2)is a factor of X3+ax2+bx+16 and b=4a.find a and b.

if x-2 is a factor then, f(2) = 0

That is, 8+4a+2b+16 = 0

Or, 4a+2b = -24

Or, 4a + 8a = -24

Or, 12a = -24

Or, a = -2

And, b = 4(-2) = -8.