- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP
- Physics
- Chemistry
- Biology
- Mathematics
- English
- Economics
- Psychology
- Social Studies
- Fashion 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

# Give examples of polynomials $p(x), g(x), q(x)$ and $r(x)$, which satisfy the division algorithm and(i) deg $p(x) =$ deg $q(x)$

**(ii)** deg $q(x) =$ deg $r(x)$

**(iii)** deg $r(x) = 0$

To do:

We have to give examples of polynomials $p(x), g(x), q(x)$ and $r(x)$, which satisfy the division algorithm and

(i) deg $p(x) =$ deg $q(x)$

(ii) deg $q(x) =$ deg $r(x)$

(iii) deg $r(x) = 0$

Solution:

(i) $p(x), g(x), q(x), r(x)$

deg $p(x) =$ deg $q(x)$

Both $g(x)$ and $r(x)$ are constant terms.

$p(x) = 2x^2+2x + 4$

$g(x) = 2$

$q(x) = x^2 + x + 2$

$r(x) = 0$

(ii) $p(x), g(x), q(x), r(x)$

deg $q(x) =$ deg $r(x)$

This is possible when degrees of both $q(x)$ and $r(x)$ are less than $p(x)$ and $g(x)$.

$p(x) = x^3+ x^2 + x + 1$

$g(x) = x^2 - 1$

$q(x) = x + 1$

$r(x) = x + 2$

(iii) $p(x), g(x), q(x), r(x)$

deg $r(x) = 0$

This is possible when product of $q(x)$ and $g(x)$ form a polynomial whose degree is equal to degree of $p(x)$ and constant term.

- Related Questions & Answers
- Construct SLR (1) parsing table for the following grammar S → x A y |x B y |x A z A → q s | q B → q
- Minimum positive integer value possible of X for given A and B in X = P*A + Q*B in C++
- Difference between x++ and x = x+1 in Java
- Difference between x++ and x= x+1 in Java programming
- Sum of the Series 1 + x/1 + x^2/2 + x^3/3 + .. + x^n/n in C++
- Write a C macro PRINT(x) which prints x
- Find minimum x such that (x % k) * (x / k) == n in C++
- Differences between Python 2.x and Python 3.x?
- Difference between %p and %x in C/C++
- Find larger of x^y and y^x in C++
- Important differences between Python 2.x and Python 3.x with examples
- Count of values of x <= n for which (n XOR x) = (n – x) in C++
- How to deal with error “var(x) : Calling var(x) on a factor x is defunct.” in R?
- Absolute difference between the first X and last X Digits of N?
- C++ Program to calculate the value of sin(x) and cos(x)
- Count Distinct Non-Negative Integer Pairs (x, y) that Satisfy the Inequality x*x + y*y < n in C++

Advertisements