![Trending Articles on Technical and Non Technical topics](/images/trending_categories.jpeg)
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies
- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who
Check if polynomial ($x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$) is divided by ($x\ +\ 1$).
Given: $x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$
To check: Here we have to check if polynomial ($x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$) is divided by ($x\ +\ 1$).
Solution:
If $x\ +\ 1$ is a factor, then $x\ =\ -1$ should be a zero of the polynomial $x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$.
Putting $x\ =\ -1$ in $x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$:
$x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$
$=\ (-1)^{3} \ +\ 3(-1)^{2} \ +\ 3(-1)\ +\ 1$
$=\ -1\ +\ 3(1) \ -\ 3\ +\ 1$
$=\ -1\ +\ 3 \ -\ 2$
$=\ 0$
It is clear that $x\ +\ 1$ is a factor of $x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$.
So, polynomial ($x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1$) is divisible by ($x\ +\ 1$).
Advertisements