If x+2a is a factor of x^{5}-4a^{2}x^{3}+2x+2 | vedclass

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Question

(A) Let $p(x) = x^{5}-4a^{2}x^{3}+2x+2a+3$.According to the Factor Theorem,if $(x+2a)$ is a factor of $p(x)$,then $p(-2a) = 0$.Substituting $x = -2a$

Vedclass · Accepted Answer

$\frac{3}{2}$

Vedclass · Answer

(A) Let $p(x) = x^{5}-4a^{2}x^{3}+2x+2a+3$.According to the Factor Theorem,if $(x+2a)$ is a factor of $p(x)$,then $p(-2a) = 0$.Substituting $x = -2a$ into the polynomial:$p(-2a) = (-2a)^{5} - 4a^{2}(-2a)^{3} + 2(-2a) + 2a + 3$$p(-2a) = -32a^{5} - 4a^{2}(-8a^{3}) - 4a + 2a + 3$$p(-2a) = -32a^{5} + 32a^{5} - 2a + 3$$p(-2a) = -2a + 3$Since $p(-2a) = 0$,we have:$-2a + 3 = 0$$2a = 3$$a = \frac{3}{2}$

If $x+2a$ is a factor of $x^{5}-4a^{2}x^{3}+2x+2a+3$,find $a$.

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