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one factor of (x+1) (x-2) (x+3) (X+4)+40is
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f(1) = 2 * -1 * 2 * 4 * 5 + 40 = 0 so (x-1) is a factor
i'm assuming that x = X
$$(x + 1) (x - 2) (x + 3) (x + 4) + 40 $$$$= 16-26 x+3 x^2+6 x^3+x^4= (-1+x) \left(-16+10 x+7 x^2+x^3\right )$$
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