A=(x−1)(x+6)(x+2)(x+3)=(x2+5x−6)(x2+5x+6)

=(x2+5x)2−62=(x2+5x)2−36≥−36

Then the minimum of A=-36

\(A=\left(x-1\right)\left(x+6\right)\left(x+2\right)\left(x+3\right)\)\(=\left(x^2+5x-6\right)\left(x^2+5x+6\right)\)

\(=\left(x^2+5x\right)^2-6^2=\left(x^2+5x\right)^2-36\ge-36\)

Then the minimum of A=-36