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).


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