Question:

If $\begin{vmatrix}x-4&2x&2x\\2x&x-4&2x\\2x&2x&x-4\end{vmatrix}=(A+Bx)(x-A)^2$, then the ordered pair $(A,B)$ is equal to

$(4,5)$

$(-4,-5)$

$(-4,3)$

$(-4,5)$

Step-by-Step Solution

Key Concept: $\det=(a+2b)(a-b)^2$ where $a=x-4$, $b=2x$. $a+2b=5x-4$, $a-b=-(x+4)$. So $\det=(5x-4)(x+4)^2$.

$(A,B)=(-4,5)$.

Correct Answer: 4