Question
Find the remainder when $x^3+3 x^3+3 x+1$ is divided by: $x+\pi$
✓
Answer
Here, $f(x)=x^3+3 x^2+3 x+1$ By remainder theorem $x+\pi=0$
$\Rightarrow x=-\pi$
Substitute the value of $x$ in $f(x) f(-\pi)=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
$=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
$\Rightarrow x=-\pi$
Substitute the value of $x$ in $f(x) f(-\pi)=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
$=(-\pi)^3+3(-\pi)^2+3(-\pi)+1$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Simplify : $2 \sqrt{48}-\sqrt{75}-\frac{1}{\sqrt{3}}$
→Factorize:
$xy^9 - yx^9$
→$xy^9 - yx^9$
In the following, using the remainder theorem, find the remainder when $f(x)$ is divided by $g(x)$ and verify the by actual division:
$f(x) = 4x^3 - 12x^2 + 14x - 3, g(x) = 2x - 1$
→$f(x) = 4x^3 - 12x^2 + 14x - 3, g(x) = 2x - 1$
In figure ABC and BDE are two equilateral triangles such that D is the midpoint of BC. AE intersects BC in F. Prove that: 
$\text{ar}(\triangle\text{BFE})=2\text{ar}(\triangle\text{EFD})$
→$\text{ar}(\triangle\text{BFE})=2\text{ar}(\triangle\text{EFD})$In a parallelogram ABCD, $\angle \text{D}=135^\circ$. Determine the measures of $\angle\text{A}$ and $\angle\text{B}$.
→Give two rational numbers lying between 0.515115111511115 and 0. 5353353335...
Rationalize the denominator : $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$
→Factorize the following expressions:
$125 + 8x^3 - 27y^3 + 90xy$
→$125 + 8x^3 - 27y^3 + 90xy$
If $\frac{a}{3}=\frac{b}{2}$ then find the value of the ratio $\frac{5 a+3 b}{7 a-2 b}$.
→If $a, b, c$ are in continued proportion then show that $\frac{a}{c}=\frac{a^2+a b+b^2}{b^2+b c+c^2}$
→