Factoring $(x+1)(x+2)(x+3)(x+4)+1$ I have to factor this polynomial:
$$(x+1)(x+2)(x+3)(x+4)+1$$
WolframAlpha gives 
$$(x^2+5x+5)^2$$
How can I prove it without expanding the result?
Thanks!

Evaluate both polynomials at $x = -1, -2, -3,$ and $-4$. They are equal at these four values, and their leading coefficients are both equal to $1$. So they are the same polynomial.
