Question

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

Answer 1

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