Question

What is the remainder when $n^2+13n+2$ is divided by $(3n+5)$.

Answer 1

Divident$=n^2+13n+2$

Division$=3n+5$

$3n+5)n^2+13n+2(n/3+\frac{34}{9}$

$n^2+\frac{5n}{3}$

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$\frac{34n}{3}+2$

$\frac{34n}{3}+\frac{170}{9}$

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$\frac{-152}{9}$

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Remainder$=\frac{-152}{9}$

Verifying by Remainder theorem

$3n+5=0$

$n=-5/3$

Put $n=-5/3$ in dividend

${(-5/3)}^2+13(-5/3)+2$

$=\frac{25}{9}-\frac{65}{3}+2$

$=\frac{25-195+18}{9}$

$=\frac{-195+43}{9}$

$=\frac{-152}{9}$.