Here is a trick to factor x^3 + 1

subtract x and add x

1) x^3 - x + x + 1

group

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

factor

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

4) x(x - 1)(x + 1) + (x + 1)

5) (x + 1)[x(x -1) + 1]

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

The same clever use of 0 can help you factor x^3 - 1

Clever use of 0 can help you factor x^4 + x^2 + 1 by subtracting and adding x

1) x^4 + x + x^2 - x + 1

group

2) (x^4 + x) + (x^2 - x + 1)

factor

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

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

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

Many other factorizations are possible using 0