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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Updated on: 10-Oct-2022

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