Question
Find the remainder when $x^3 + 3x^3 + 3x + 1$ is divided by: $\text{x}+\pi$
✓
Answer
Here,
$f(x) = x^3 + 3x^2 + 3x + 1$
By remainder theorem
$\text{x}+\pi=0$
$\Rightarrow\ \text{x}=-\pi$
Substitute the value of $x$ in $f(x)$
$\text{f}(-\pi)=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
$=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
$f(x) = x^3 + 3x^2 + 3x + 1$
By remainder theorem
$\text{x}+\pi=0$
$\Rightarrow\ \text{x}=-\pi$
Substitute the value of $x$ in $f(x)$
$\text{f}(-\pi)=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
$=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
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