Q. 1 A

I/we factorise the following algebraic expressions:

x2 + 5x + 6

Answer :

An algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.

And, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind.


Let’s factorize the given algebraic expression.


We have x2 + 5x + 6.


First: Multiply the coefficient of x2 and the constant.


Coefficient of x2 = 1


Constant = 6


1 × 6 = 6 …(a)


Now, Observe the coefficient of x = 5


We need to split the value obtained at (a), such that the sum\difference of the split numbers comes out to be 5.


To split: We need to find the factors of 6.


Factors of 6 = 2, 3


Add 2 and 3 = 2 + 3 = 5


Multiply 2 and 3 = 2 × 3 = 6


Since, the sum of 2 and 3 is 5 and multiplication is 6. So, we can write


x2 + 5x + 6 = x2 + (3x + 2x) + 6


x2 + 5x + 6 = x2 + 3x + 2x + 6


x2 + 5x + 6 = (x2 + 3x) + (2x + 6)


Now, take out common number or variable in first two pairs and the last two pairs subsequently.


x2 + 5x + 6 = x(x + 3) + 2(x + 3)


Now, take out the common number or variable again from the two pairs.


x2 + 5x + 6 = (x + 3)(x + 2)


Thus, the factorization of x2 + 5x + 6 = (x + 3)(x + 2).


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Master Algebraic Identities43 mins
Division of Algebraic Expressions37 mins
Division of Algebraic Expressions36 mins
Operations on Algebraic Expressions51 mins
How to Use Algebraic Identities40 mins
Genius Quiz | Algebraic Expressions and Identities30 mins
Champ Quiz | Division of Polynomials33 mins
Quiz | Questions on Factorization41 mins
Algebraic Identities - Mark your Weak Areas41 mins
Quiz | Important Questions on Factorisation35 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses