Question

Factorise the following:

6x² – 15x – 9

Answer 1

We are given the expression:

6x² – 15x – 9

Step 1: Factor out the common factor:

The greatest common factor (GCF) in all terms is 3.

Let’s factor out 3:

3(2x² – 5x – 3)

Step 2: Factor the quadratic expression:

Now, we need to factor 2x² – 5x – 3.

We are looking for two numbers that multiply to 2 × –3 = –6 (the product of the coefficient of x² and the constant term) and add up to –5 (the coefficient of x).

The two numbers that satisfy this are –6 and 1 because:

–6 × 1 = –6 and –6 + 1 = –5

Step 3: Rewrite the middle term:

We can now rewrite –5x as –6x + x:

2x² – 6x + x – 3

Step 4: Group the terms:

Now, group the terms in pairs:

(2x² – 6x) + (x – 3)

Step 5: Factor each group:

Factor out the common factor from each group:

2x(x – 3) + 1(x – 3)

Step 6: Factor out the common binomial:

Now, factor out the common binomial factor (x – 3):

(2x + 1) (x – 3)

Final factorisation

Now, put back the factor of 3 that we factored out initially:

3(2x + 1) (x – 3)

Thus, the fully factorised form is 3(2x + 1) (x – 3)