બહુપદી $p(x)=3 x^{3}+7 x$ નું શૂન્ય $7+3x$ છે.

$\left[\because 7+3 x=0, \,\therefore 7=-3 x, \,\therefore x=-\frac{7}{3}\right]$

$p(x) =3 x^{3}+7 x $

$\therefore p\left(-\frac{7}{3}\right) =3\left(-\frac{7}{3}\right)^{3}+7\left(-\frac{7}{3}\right)$

$=3\left(-\frac{343}{27}\right)+7\left(-\frac{7}{3}\right)$

$=\frac{-343}{9}+\left(\frac{-49}{3}\right) $

$=\frac{-343+(-147)}{9}=\frac{-343-147}{9}=-\frac{490}{9}$

$-\frac{490}{9} \neq 0$ તેથી $3 x^{3}+7 x$ નો અવયવ $7+3 x$ નથી.

આમ, શેષ શૂન્ય ન હોવાથી $7+3x$ નો અવયવ $7+3x$ નથી.