- Trending Categories
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
Factorize the following algebraic expressions:
(i) $x^2-22x+120$
(ii) $x^2-11x-42$
Given:
The given expressions are:
(i) $x^2-22x+120$
(ii) $x^2-11x-42$
To do:
We have to factorize the given algebraic expressions.
Solution:
Factorizing algebraic expressions:
Factorizing an algebraic expression implies writing the expression as a product of two or more factors. Factorization is the reverse of distribution.
An algebraic expression is factored completely when it is written as a product of prime factors.
(i) The given expression is $x^2-22x+120$.
We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.
$x^2-22x+120$ can be written as,
$x^2-22x+120=x^2-12x-10x+120$ [Since $-22x=-12x-10x$ and $x^2 \times 120=-12x \times (-10x) =120x^2$]
$x^2-22x+120=x(x-12)-10(x-12)$
$x^2-22x+120=(x-12)(x-10)$
Hence, the given expression can be factorized as $(x-12)(x-10)$.
(ii) The given expression is $x^2-11x-42$.
We can factorize the given expression by splitting the middle term. Splitting the middle term means we have to rewrite the middle term as the sum or difference of the two terms.
$x^2-11x-42$ can be written as,
$x^2-11x-42=x^2+3x-14x-42$ [Since $-11x=3x-14x$ and $x^2 \times (-42)=3x \times (-14x) =-42x^2$]
$x^2-11x-42=x(x+3)-14(x+3)$
$x^2-11x-42=(x+3)(x-14)$
Hence, the given expression can be factorized as $(x+3)(x-14)$.
373 Views
