The expression $x^3 + 1$ can be factored using the sum of cubes formula. The sum of cubes formula is:

$x^3 + y^3 = (x + y)(x^2 - xy + y^2)$

For $x^3 + 1$:

• $x = x$
• $y = 1$ because $1 = 1^3$

Applying the formula:

$x^3 + 1 = x^3 + 1^3 = (x + 1)(x^2 - x \cdot 1 + 1^2)$

Simplifying further:

$x^3 + 1 = (x + 1)(x^2 - x + 1)$

So, the factored form of $x^3 + 1$ is:

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

Would you like more details or have any questions?

Here are 5 related questions:

1. How do you factor $x^3 - 1$?
2. What is the difference between the sum of cubes and the difference of cubes?
3. How do you find the roots of the equation $x^3 + 1 = 0$?
4. Can the sum of cubes be applied to higher powers like $x^6 + 1$?
5. How would you factor $8x^3 + 1$?

Tip: When dealing with cubes, always identify if it's a sum or difference of cubes to apply the appropriate formula.