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

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Answer 1 · 2016-05-05T18:59:15

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

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 $(1/2+x)$ :

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

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