How to factor polynomial
u^2+uv+v^2

This polynomial can't be factored further. the three terms have nothing in common that make it factorable--you can't take anything out of all three terms.

however, if you perhaps mistyped and meant u² + 2uv + v², you would be able to factor it into (u + v)(u + v).

Is there a picture?
To go with this question?