(X+2)(X+3)(X+4)(X+5)+1

是不是因式分解
(X+2)(X+3)(X+4)(X+5)+1
=(x+2)(x+5)(x+3)(x+4)+1
=(x^+7x+10)(x^+7x+12)+1
=(x^+7x)^+22(x^+7x)+120+1
=(x^+7x+11)^

(X+2)(X+3)(X+4)(X+5)+1
=(x^2+7x+12)(x^2+7x+10)+1
=(x^2+7x+10)^2+2(x^2+7x+10)+1
=(x^2+7x+10+1)^2
=(x^2+7x+11)^2
=(x+(7-√5)/2)^2*(x+(7+√5)/2)^2

=(x^2+5*x+6)(x^2+9*x+20)+1
=(x^4+9*x^3+20*x^2+5*x^3+45*x^2+100*x+6*x^2+54*x+120)+1
=x^4+14*x^3+71*x^2+154*x+121
=x(x^3+14*x^2+71*x+154)+121

不知道，对不对

=（x^2+5x+6)(x^2+9x+20)+1
=x^4+9x^3+20x^2+5x^3+45x^2+100x+6x^2+45x+120+1
=x^4+14x^3+74x^2+45x+121