Question

How do you factor `x^4 + 10x^2 + 9`?

Answer 1

Substitute `u = x^2` and factor as normally.

1. `x^4 + 10x^2 + 9` Given
2. `u^2 + 10u +9` **Substitute `u=x^2` **
3. `(u+9)(u+1)` Factor
4. `(x^2+9)(x^2+1)` **Substitute Back `u=x^2` **

If you wish to continue to imaginary linear factors:

1. `(x+3i)(x-3i)(x+i)(x-i)` .