Question

Factorise the following:

4a² – 12a – 216

Answer 1

To factorise the quadratic expression:

4a² – 12a – 216

Step 1: Check for a common factor.

All terms are divisible by 4:

4a² – 12a – 216

= 4(a² – 3a – 54)

Step 2: Factorise the quadratic inside the bracket.

We need two numbers that multiply to –54 and add up to –3.

These are 6 and –9:

a² – 3a – 54

= (a + 6) (a – 9)

Step 3: Combine the factorised form with the common factor.

4a² – 12a – 216

= 4(a + 6) (a – 9)

4(a + 6) (a – 9)