Factor x^3-8

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

Expression

Answer

(x - 2)(x^2 + 2x + 4)

To factor x^3-8, recognize this as a difference of two cubes — each term is a perfect cube.

x³-8

Step 1 — Verify both terms are perfect cubes

Check: is x^3 a perfect cube? x³ = x^3 ✓

Check: is 8 a perfect cube? 2³ = 8 ✓

Step 2 — Apply the difference of cubes formula

The difference of cubes formula states:

a³ − b³ = (a − b)(a² + ab + b²)

With a = x and b = 2:

Step 3 — Compute each part

First factor: a − b = x − 2

Second factor: a² + ab + b² = x^2 + 2x + 4

Note: the trinomial x^2 + 2x + 4 cannot be factored further over the real numbers.

Step 4 — Write the factored form

= (x − 2)(x² + 2x + 4)

(x - 2)(x² + 2x + 4)

How to factor x^3-8

To factor x^3-8, identify the type of polynomial and apply the appropriate technique. The factored form is (x - 2)(x^2 + 2x + 4).

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^3-8?
The answer is (x - 2)(x^2 + 2x + 4).

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