For the polynomial 3x2+ax–12 to be completely divisible by the polynomial x–8 , we need to satisfy the following condition: The remainder should be 0, on dividing the former polynomial with the latter. We take x–8 as the divisor, and 3x2+ax–12 as the dividend.
We obtain the remainder as: (a+22.5)x=0 ⇒a=−22.5 ∴ The required value of a is -22.5