Question

Factors of x³ – 3x² – x + 3 are ______.

Options

• (x – 1) (x + 1) (x – 3)

• (x – 1) (x + 1) (x + 3)

• (x – 1) (x + 2) (x – 3)

• (x – 1) (x – 2) (х – 3)

Answer 1

Factors of x³ – 3x² – x + 3 are (x – 1) (x + 1) (x – 3).

Explanation:

• To factor x³ – 3x² – x + 3, one method is to group terms and factor by grouping.
• Group as (x³ – 3x²) – (x – 3).
• Factor out (x²) from the first group: x²(x – 3).
• Factor out (–1) from the second group: –1(x – 3).
• Now factor out the common binomial (x – 3): (x – 3)(x² – 1).
• Recognize that (x² – 1) is a difference of squares: (x – 1)(x + 1).
• Therefore, the complete factorization is (x – 3)(x – 1)(x + 1).