Question

How do you factor `1/4+x+x^2`?

Answer 1

`1/4+x+x^2 = (1/2+x)^2`

Explanation:

This is a perfect square trinomial.

Both `1/4 = (1/2)^2` and `x^2` are perfect squares, so the only remaining question is whether the middle term matches when you square `(1/2+x)`:

`(1/2+x)^2 = (1/2)^2+2(1/2)x + x^2 = 1/4+x+x^2`