I/we factorise the following algebraic expressions:

x² + 5x + 6

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 sumdifference 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).