Question

Factorise the following:

5a² – 10a – 15

Answer 1

To factorise 5a² – 10a – 15, we start by factoring out the greatest common factor (GCF) of the terms.

The GCF of 5a² – 10a and –15 is 5.

So, factor out 5 from the expression 5(a² – 2a – 3)

Now, we need to factor a² – 2a – 3.

We are looking for two numbers that multiply to –3 and add up to –2.

These numbers are –3 and 1, because –3 × 1 = –3 and –3 + 1 = –2.

So, we can rewrite a² – 2a – 3 as (a – 3)(a + 1)

Thus, the fully factorized form of 5a² – 10a – 15 is 5(a – 3)(a + 1)