How do you factor $x^2+x+3$ ?

Question

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Answer 1 · 2015-04-12T22:28:49

This expression has no real factors

But if you really want to factorize you can obtain complex factors

Method

Find the roots using the quadratic formula

$x = (-1 +- srqt(1 - 14))/2$

$=> x = -1/2 +- sqrt(-13)/2$

$=> x = -1/2 +- (13i)/2$

Therefore,

$x = -1/2 + (13i)/2 => x + 1/2 - (13i)/2 = 0$
and
$x = -1/2 - (13i)/2 => x + 1/2 + (13i)/2 = 0$

Hence,

$(x + 1/2 - (13i)/2)(x + 1/2 + (13i)/2) = 0$

Therefore Factorizing $x^2 + x + 3 = (x + 1/2 - (13i)/2)(x + 1/2 + (13i)/2)$

How do you factor x^2+x+3x^2+x+3?