Question

Factorise:

x³ – 5x² – 9x + 45

Answer 1

We are given the expression:

x³ – 5x² – 9x + 45

Step 1: Group the terms

We can start by grouping the terms in pairs:

(x³ – 5x²) – (9x – 45)

Step 2: Factor each group

Factor out the common factors from each group:

x²(x – 5) – 9(x – 5)

Step 3: Factor out the common binomial factor

Now, we can factor out the common binomial factor (x – 5):

(x – 5) (x² – 9)

Step 4: Recognize the difference of squares

The expression x² – 9 is a difference of squares, so we can factor it further:

x² – 9 = (x – 3) (x + 3)

Final factorisation:

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