\(A=-\left(x-1\right)\left(x+6\right)\left(x+2\right)\left(x+3\right)+45\)
\(A=-\left(x^2+5x-6\right)\left(x^2+5x+6\right)+45\)
\(A=36-\left(x^2+5x\right)^2+45\)
\(A=81-\left(x^2+5x\right)^2\le81\)
\(\Rightarrow A_{max}=81\) khi \(\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\)