I/we factorise the following algebraic expressions:

p² + 3p – 18

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 p² + 3p – 18.

First: Multiply the coefficient of p² and the constant.

Coefficient of p² = 1

Constant = -18

⇒ 1 × -18 = -18 …(a)

Now, Observe the coefficient of p = 3

We need to split the value obtained at (a), such that the sum/difference of the split numbers comes out to be 3.

To split: We need to find the factors of -18.

Factors of -18 = 2, 3, 3, -1

Add (2 × 3 =) 6 and (3 × -1 =) -3 = 6 + (-3) = 3

Multiply 6 and -3 = 6 × -3 = -18

Since, the sum of 6 and -3 is 3 and multiplication is -18. So, we can write

p² + 3p – 18 = p² + (6p – 3p) – 18

⇒ p² + 3p – 18 = p² + 6p – 3p – 18

⇒ p² + 3p – 18 = (p² + 6p) + (-3p – 18)

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

⇒ p² + 3p – 18 = p(p + 6) -3(p + 6)

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

⇒ p² + 3p – 18 = (p + 6)(p – 3)

Thus, the factorization of p² + 3p – 18 = (p + 6)(p – 3).