Find the remainder when x^3 + 3x^3 + 3x + 1 is divided by:5 + 2x - Vidyadip

Question

Find the remainder when $x^3 + 3x^3 + 3x + 1$ is divided by:$5 + 2x$

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Answer

Here, $f(x) = x^3 + 3x^2 + 3x + 1$ By remainder theorem $5 + 2x = 0 2x = -5$
$\text{x}=\frac{-5}{2}$ substitute the value of $x$ in $f(x)$ $\text{f}\Big(\frac{-5}{2}\Big)=\Big(\frac{-5}{2}\Big)^3+3\Big(\frac{-5}{2}\Big)+1$
$=\frac{-125}{8}+3\Big(\frac{25}{4}\Big)+3\Big(\frac{-5}{2}\Big)+1$
$=\frac{-125}{8}+\frac{75}{4}-\frac{15}{2}+1$
Taking $L.C.M$ $=\frac{-125+150-50+8}{8}$
$=\frac{-27}{8}$

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