Factor A Degree 100 Polynomial (III)

Algebra Level 5

Can the polynomial (x1)(x2)(x3)(x100)+1+101! (x-1)(x-2)(x-3) \cdots (x-100) + 1 + 101! be factorized into 2 non-constant polynomials with integer coefficients?

Note: 101!=1×2××101101! = 1\times2\times\cdots\times101.


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