I/we factorise the following algebraic expressions:

x² – x – 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 – x – 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 = -1

We need to split the value obtained at (a), such that the sum/difference of the split numbers comes out to be -1.

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

Factors of -6 = 2, 3, -1

Add (3 × -1 =) -3 and 2 = -3 + 2 = -1

Multiply -3 and 2 = -3 × 2 = -6

Since, the sum of 2 and -3 is 1 and multiplication is -6. So, we can write

x² – x – 6 = x² – (2x – 3x) – 6

⇒ x² – x – 6 = x² – 2x + 3x – 6

⇒ x² – x – 6 = (x² – 2x) + (3x – 6)

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

⇒ x² – x – 6 = x(x – 2) + 3(x – 2)

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

⇒ x² – x – 6 = (x – 2)(x + 3)

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