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 and (2 × -1 =) -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 + (3x – 2x) – 6

⇒ x² + x – 6 = x² + 3x – 2x – 6

⇒ x² + x – 6 = (x² + 3x) + (-2x – 6)

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

⇒ x² + x – 6 = x(x + 3) – 2(x + 3)

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

⇒ x² + x – 6 = (x + 3)(x – 2)

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