Examples on Factorization of Algebraic Expression
Example 1: x2 + 5x + 6
Solution:
To factorize the expression x2 + 5x + 6, we need to find two numbers that multiply to give us 6 and add to give us 5.
The two numbers are 2 and 3, because 2 × 3 = 6 and 2 + 3 = 5.
So, we can rewrite the expression as:
x2 + 5x + 6 = (x + 2)(x + 3)
Thus, the factorization of x2 + 5x + 6 is (x + 2)(x + 3).
Example 2: x2 – 4
Solution:
To factorize the expression x2 – 4, we can use identity i.e.,
a2 – b2 = (a+b)(a−b)
So, x2 – 4 = x2 – 22 = (x + 2)(x – 2).
Example 3: x3 + 3x2 + 2x + 6
Solution:
To factorize the expression x3 + 3x2 + 2x + 6, we group the terms:
(x3 + 3x2) + (2x + 6)
= x2(x + 3) + 2(x + 3)
= (x2 + 2)(x + 3)
So, x3 + 3x2 + 2x + 6 = (x2 + 2)(x + 3).
Factorization of Algebraic Expression
In algebra, factorization is a fundamental concept that helps in simplifying expressions and solving equations. Factorization involves breaking down algebraic expressions into simpler components, which aids in understanding their structure and properties.
In this article, we’ll look at basic methods and examples for factorizing algebraic expressions.
Table of Content
- What are Expressions?
- What is Factorization of Algebraic Expressions?
- How to Factorize Algebraic Expressions?
- Factorization using Common Factors
- Factoring by Regrouping Terms
- Factorization Using Standard Identities
- Real-Life Examples of Factorization