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
Divide:
(i) $6x^3y^2z^2$ by $3x^2yz$
(ii) $15m^2n^3$ by $5m^2n^2$
(iii) $24a^3b^3$ by $-8ab$
Given:
The given expressions are:
(i) $6x^3y^2z^2$ by $3x^2yz$
(ii) $15m^2n^3$ by $5m^2n^2$
(iii) $24a^3b^3$ by $-8ab$
To do:
We have to divide the given expressions.
Solution:
We have to divide the given polynomials by monomials using the formula $x^a \div x^b=a^{a-b}$
Polynomials:
Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.
Monomial:
A monomial is an expression that contains a single term composed of a product of constants and variables with non-negative integer exponents.
Therefore,
(i) The given expression is $6x^3y^2z^2$ by $3x^2yz$.
$6x^3y^2z^2 \div 3x^2yz=\frac{6}{3}x^{3-2}y^{2-1}z^{2-1}$
$6x^3y^2z^2 \div 3x^2yz=2x^{1}y^{1}z^{1}$
$6x^3y^2z^2 \div 3x^2yz=2xyz$
Hence, $6x^3y^2z^2$ divided by $3x^2yz$ is $2xyz$.
(ii) The given expression is $15m^2n^3$ by $5m^2n^2$.
$15m^2n^3 \div 5m^2n^2=\frac{15}{5}m^{2-2}n^{3-2}$
$15m^2n^3 \div 5m^2n^2=3m^{0}n^{1}$
$15m^2n^3 \div 5m^2n^2=3n$
Hence, $15m^2n^3$ divided by $5m^2n^2$ is $3n$.
(iii) The given expression is $24a^3b^3$ by $-8ab$.
$24a^3b^3 \div (-8ab)=\frac{24}{-8}a^{3-1}b^{3-1}$
$24a^3b^3 \div (-8ab)=-3a^{2}b^{2}$
Hence, $24a^3b^3$ divided by $-8ab$ is $-3a^{2}b^{2}$.
140 Views
