(x-2)(x-3)(x-4)(x-5)+1
=(x-2)(x-5)(x-3)(x-4)+1
=(x^2-7x+10)(x^2-7x+12)+1
=(x^2-7x)^2+22(x^2-7x)+121
=(x^2-7x)^2+22(x^2-7x)+11^2
=[(x^2-7x)+11]^2