Question
Find the remainder when $x^3+3 x^2+3 x+1$ is divided by $5+2 x$.
✓
Answer
$\text { Let } p(x)=x^3+3 x^2+3 x+1$
$5+2 x=0$
$\Rightarrow 2 x=-5$
$\Rightarrow x=-\frac{5}{2}$
$=\left(-\frac{5}{2}\right)^3+3\left(-\frac{5}{2}\right)^2+3\left(-\frac{5}{2}\right)+1$
$=-\frac{125}{8}+\frac{75}{4}-\frac{15}{2}+1=-\frac{27}{8}$
$5+2 x=0$
$\Rightarrow 2 x=-5$
$\Rightarrow x=-\frac{5}{2}$
$=\left(-\frac{5}{2}\right)^3+3\left(-\frac{5}{2}\right)^2+3\left(-\frac{5}{2}\right)+1$
$=-\frac{125}{8}+\frac{75}{4}-\frac{15}{2}+1=-\frac{27}{8}$
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