Question

Factorise the following:

x³ – 3x² – 2x + 6

Answer 1

Given expression: x³ – 3x² – 2x + 6

Step-wise calculation:

1. Group the terms:

(x³ – 3x²) + (–2x + 6) ]

2. Factor each group:

x²(x – 3) – 2(x – 3)

3. Take the common factor (x – 3):

(x – 3)(x² – 2)

4. Recognize (x² – 2) can be written as `(x - sqrt(2))(x + sqrt(2))` if further factorization over the reals is considered.

x³ – 3x² – 2x + 6 = (x – 3)(x² – 2)

or fully factored over the reals,

= `(x - 3)(x - sqrt(2))(x + sqrt(2))`