Question
Find the remainder when $x^3 + 3x^3 + 3x + 1$ is divided by:$5 + 2x$
✓
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 $\text{L.C.M}$
$=\frac{-125+150-50+8}{8}$
$=\frac{-27}{8}$
$f(x) = x^3 + 3x^2 + 3x + 1$
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 $\text{L.C.M}$
$=\frac{-125+150-50+8}{8}$
$=\frac{-27}{8}$
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