If x+a is a factor of the polynomial x^{3}+a | vedclass

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(A) Let $p(x) = x^{3} + a x^{2} - 2 x + a + 4$.Since $(x+a)$ is a factor of $p(x)$,by the Factor Theorem,$p(-a) = 0$.Substituting $x = -a$ into the po

Vedclass · Accepted Answer

$-\frac{4}{3}$

Vedclass · Answer

(A) Let $p(x) = x^{3} + a x^{2} - 2 x + a + 4$.Since $(x+a)$ is a factor of $p(x)$,by the Factor Theorem,$p(-a) = 0$.Substituting $x = -a$ into the polynomial:$p(-a) = (-a)^{3} + a(-a)^{2} - 2(-a) + a + 4 = 0$$-a^{3} + a(a^{2}) + 2a + a + 4 = 0$$-a^{3} + a^{3} + 3a + 4 = 0$$3a + 4 = 0$$3a = -4$$a = -\frac{4}{3}$.

If $x+a$ is a factor of the polynomial $x^{3}+a x^{2}-2 x+a+4$,then find the value of $a$.

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