(A) According to the Factor Theorem,if $(x-c)$ is a factor of a polynomial $p(x)$,then $p(c) = 0$.Here,$p(x) = x^{3} + 7x^{2} + ax - 3$ and the factor

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(A) According to the Factor Theorem,if $(x-c)$ is a factor of a polynomial $p(x)$,then $p(c) = 0$.Here,$p(x) = x^{3} + 7x^{2} + ax - 3$ and the factor is $(x-1)$,so $c = 1$.Setting $p(1) = 0$:$(1)^{3} + 7(1)^{2} + a(1) - 3 = 0$$1 + 7 + a - 3 = 0$$8 + a - 3 = 0$$5 + a = 0$$a = -5$