(D) Given the polynomial $p(x) = x^{2} + x + k$.According to the Factor Theorem,if $(x - 1)$ is a factor of $p(x)$,then $p(1)$ must be equal to $0$.Su

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(D) Given the polynomial $p(x) = x^{2} + x + k$.According to the Factor Theorem,if $(x - 1)$ is a factor of $p(x)$,then $p(1)$ must be equal to $0$.Substituting $x = 1$ into the polynomial:$p(1) = (1)^{2} + 1 + k$$p(1) = 1 + 1 + k$$p(1) = 2 + k$Since $p(1) = 0$,we have:$2 + k = 0$$k = -2$