Madhya Pradesh Police Exam Model Paper 10

For the polynomial $3{\mathit{x}}^2+\mathit{a}\mathit{x}\mathit{–}12$ to be completely divisible by the polynomial $\mathit{x}\mathit{–}8$ , we need to satisfy the following condition:
The remainder should be 0, on dividing the former polynomial with the latter.
We take $\mathit{x}\mathit{–}8$ as the divisor, and $3{\mathit{x}}^2+\mathit{a}\mathit{x}\mathit{–}12$ as the dividend.We obtain the remainder as:
$\left(\mathit{a}+22.5\right)\mathit{x}=0$
$\Rightarrow \mathit{a}=-22.5$
∴ The required value of a is -22.5