Factor x^4-1

Factor polynomials completely: trinomials, difference of squares, sum/difference of cubes.

Expression

Answer

(x - 1)(x + 1)(x^2 + 1)

To factor x^4-1, look for patterns like grouping, difference of squares, or rational roots.

x⁴-1

Step 1 — Recognize as a difference of squares

Treat x⁴ as (x²)² and 1 as (1)². Apply a² − b² = (a − b)(a + b):

(x²)² − 1² = (x² − 1)(x² + 1)

Step 2 — Factor x² − 1 further

x² − 1 is itself a difference of squares:

x² − 1 = (x − 1)(x + 1)

Step 3 — Write the complete factored form

x² + 1 cannot be factored further over the reals.

= (x - 1)(x + 1)(x² + 1)

(x - 1)(x + 1)(x² + 1)

How to factor x^4-1

To factor x^4-1, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 1)(x + 1)(x^2 + 1).

This is a polynomial factoring problem — we break a polynomial into a product of simpler expressions. Common methods include GCF extraction, difference of squares, and trinomial factoring.

Frequently asked questions

What is the answer to x^4-1?
The answer is (x - 1)(x + 1)(x^2 + 1).

What method is used?
identifying the polynomial type and applying the matching technique — GCF, trinomial factoring, difference of squares, or special cube formulas.