Question

 $\left|\begin{array}{ccc}x-4& 2x& 2x\\ 2x& x-4& 2x\\ 2x& 2x& x-4\end{array}\right|$ = = (A + Bx) (x - A)²
Put x = 0 $\Rightarrow$$\left|\begin{array}{ccc}-4& 0& 0\\ 0& -4& 0\\ 0& 0& -4\end{array}\right|$ = A³ $\Rightarrow$A = - 4
$\left|\begin{array}{ccc}x-4& 2x& 2x\\ 2x& x-4& 2x\\ 2x& 2x& x-4\end{array}\right|$  = (Bx - 4) (x + 4)²
$\left|\begin{array}{ccc}1-\frac{4}{x}& 2& 2\\ 2& 1-\frac{4}{x}& 2\\ 2& 2& 1-\frac{4}{x}\end{array}\right|$$=\left(B-\frac{4}{x}\right) {\left(1+\frac{4}{x}\right)}^2$
Put x $\to \infty \Rightarrow$$\left|\begin{array}{ccc}1& 2& 2\\ 2& 1& 2\\ 2& 2& 1\end{array}\right|$ = B $\Rightarrow$ B = 5
ordered pair (A, B) is (-4, 5)