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

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Solution

7 + 3x = 0
$\Rightarrow 3 x = - 7$
$\Rightarrow x = \frac{- 7}{3}$
Substitute $x = \frac{- 7}{3}$ in p(x) = $3 x^{3} + 7 x$ .
$p (\frac{- 7}{3}) = 3 {(\frac{- 7}{3})}^{3} + 7 (\frac{- 7}{3}) = \frac{- 343}{9} - \frac{49}{3} = \frac{- 343 - 147}{9} = \frac{- 490}{9} .$
So, remainder $= \frac{- 490}{9}$ which is different from 0.
Therefore, (3x + 7) is not a factor of the polynomial $3 x^{3} + 7 x .$

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