Question

If $7+3x$ is factor of $3x^3+7x$, then the remainder is :

• A. $\frac{490}{9}$
• B. $\frac{-490}{9}$
• C. $\frac{470}{9}$
• D. None of the above

Answer 1

Answer: (B)

$\frac{-490}{9}$

Since the divisor is $3x+7$, remainder$=f\left(\frac{-7}{3}\right)$ by remainder theorem.
Thus, remainder $=3\times {\left(\frac{-7}{3}\right)}^3+7\times {\left(\frac{-7}{3}\right)}^1$
$\therefore$ Remainder $=\frac{-343}{9}+\frac{-49}{3}$
$\therefore$ Remainder $=\frac{-490}{9}$