Check whether 7+3x is a factor of 3x^3+7x. | vedclass

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(B) Let $p(x) = 3x^3 + 7x$.To check if $(7+3x)$ is a factor of $p(x)$,we find the zero of $(7+3x)$ by setting it to $0$:$7 + 3x = 0 \implies 3x = -7 \

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No

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(B) Let $p(x) = 3x^3 + 7x$.To check if $(7+3x)$ is a factor of $p(x)$,we find the zero of $(7+3x)$ by setting it to $0$:$7 + 3x = 0 \implies 3x = -7 \implies x = -\frac{7}{3}$.According to the Factor Theorem,$(7+3x)$ is a factor of $p(x)$ if and only if $p(-\frac{7}{3}) = 0$.Now,calculate $p(-\frac{7}{3})$:$p(-\frac{7}{3}) = 3(-\frac{7}{3})^3 + 7(-\frac{7}{3})$$= 3(-\frac{343}{27}) + (-\frac{49}{3})$$= -\frac{343}{9} - \frac{49}{3}$$= \frac{-343 - 147}{9} = -\frac{490}{9}$.Since $p(-\frac{7}{3}) = -\frac{490}{9} 
eq 0$,the remainder is not $0$.Therefore,$(7+3x)$ is not a factor of $3x^3+7x$.

Check whether $7+3x$ is a factor of $3x^3+7x$.

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