(x-1)(x+3)(x-4)(x-8)+1996
=[(x-1)(x-4)][(x+3)(x-8)]+1996
=(x^2-5x+4)(x^2-5x-24)+1996
=(x^2-5x)^2-20(x^2-5x)-96+1996
=(x^2-5x)^2-20(x^2-5x)+1900
=x^4-10x^3+25x^2-20x^2+100x+1900
=x^4-10x^3+5x^2+100x+1900