Question

Factorise the following:

5x² – 5x – 30

Answer 1

We are asked to factorise the expression:

5x² – 5x – 30

Step 1: Factor out the common factor:

The common factor in all terms is 5, so we can factor out 5:

5(x² – x – 6)

Step 2: Factor the quadratic expression:

Now, we need to factor x² – x – 6. We look for two numbers that multiply to –6 (the constant term) and add up to –1 (the coefficient of x).

The two numbers are –3 and 2, since –3 × 2 = –6 and –3 + 2 = –1

Step 3: Factor the quadratic expression:

Now we can factor x² – x – 6 as x² – x – 6 = (x – 3) (x + 2)

Final factorization

Now, substitute this back into the original expression:

5(x² – x – 6) = 5(x – 3) (x + 2)

Thus, the fully factorised form is 5(x – 3) (x + 2)