The correct option is A (x−6)(x+1)(x−7)(x+2)
(x2−5x)(x2−5x−20)+84=(x2−5x)(x2−5x)−20(x2−5x)+84
=(x2−5x)2−20(x2−5x)+84
Let x2−5x=a. Then, the given expression
=a2−20a+84=a2−16a−14a+84
=a(a−6)−14(a−6)=(a−6)(a−14)
=(x2−5x−6)(x2−5x−14)=(x2−6x−x+6)(x2−7x+2x−16)
=[x(x−6)+1(x−6)][x(x−7)+2(x−7)]
=(x−6)(x+1)(x−7)(x+2)