Let x5−x2−x−1=p1(x)p2(x)⋯pk(x), where each non-constant polynomial pi(x)is monic with integer coefficients, and cannot be factored further over the integers. Compute p1(2)+p2(2)+⋯+pk(2).
$p_1(2) + p_2(2) + \dots + p_k(2) = 18$
