Question

Factorise:

x³ – 3x² – 4x + 12

Answer 1

We are given the expression:

x³ – 3x² – 4x + 12

Step 1: Group the terms

We can start by grouping the terms in pairs:

(x³ – 3x²) – (4x – 12)

Step 2: Factor each group

Factor out the common factors from each group:

x²(x – 3) – 4(x – 3)

Step 3: Factor out the common binomial factor

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

(x – 3) (x² – 4)

Step 4: Recognize the difference of squares

The expression x² – 4 is a difference of squares, so we can factor it further:

x² – 4 = (x – 2) (x + 2)

Final factorisation:

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