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

Substitute $u = {x}^{2}$ and factor as normally.
1. ${x}^{4} + 10 {x}^{2} + 9$ Given
2. ${u}^{2} + 10 u + 9$ Substitute $u = {x}^{2}$
3. $\left(u + 9\right) \left(u + 1\right)$ Factor
4. $\left({x}^{2} + 9\right) \left({x}^{2} + 1\right)$ Substitute Back $u = {x}^{2}$
1. $\left(x + 3 i\right) \left(x - 3 i\right) \left(x + i\right) \left(x - i\right)$ .