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Check whether $ 7+3 x $ is a factor of $ 3 x^{3}+7 x $.
Given :
$f(x) = 3x^3 + 7x$, $g(x) = 7+3x$ are the given polynomials.
To do :
We have to check whether $3x + 7$ is a factor of $3x^3 + 7x$.
Solution :
$3x +7 = 0$
$3x = -7$
$x = \frac{-7}{3}$
If $g(x)$ is a factor of $f(x)$ then $\frac{-7}{3}= 0$.
$f(\frac{-7}{3}) = 3(\frac{-7}{3})^3+ 7(\frac{-7}{3})$
$= \frac{-343}{9} + \frac{-49}{3}$
$= \frac{-343-3(49)}{9}$
$= \frac{-343-147}{9}$
$= \frac{-490}{9}$
$f(\frac{-7}{3})$ is not equal to zero.
Therefore,
$3x+7$ is not a factor of $3x^3 + 7x$.
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