(A) Let $p(x) = x^{3} + 13x^{2} + ax + 35$.Since $x+5$ is a factor of $p(x)$,by the Factor Theorem,$p(-5) = 0$.Substituting $x = -5$ into the polynomi

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(A) Let $p(x) = x^{3} + 13x^{2} + ax + 35$.Since $x+5$ is a factor of $p(x)$,by the Factor Theorem,$p(-5) = 0$.Substituting $x = -5$ into the polynomial:$(-5)^{3} + 13(-5)^{2} + a(-5) + 35 = 0$$-125 + 13(25) - 5a + 35 = 0$$-125 + 325 - 5a + 35 = 0$$235 - 5a = 0$$5a = 235$$a = 47$.