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

Jul 30, 2015

$\left(x + 1 + i \sqrt{2}\right) \left(x + 1 - i \sqrt{2}\right)$

#### Explanation:

Solve for the roots. First complete the square:

${x}^{2} + 2 x + 3 = {\left(x + 1\right)}^{2} + 2 = 0$

Solve for $x$:

${\left(x + 1\right)}^{2} + 2 = 0$

=>

${\left(x + 1\right)}^{2} = - 2$

=>

$x + 1 = \pm i \sqrt{2}$

=>

$x = - 1 \pm i \sqrt{2}$

Therefore the factorisation is:

$\left(x + 1 + i \sqrt{2}\right) \left(x + 1 - i \sqrt{2}\right)$

Jul 30, 2015

Factor $y = {x}^{2} + 2 x + 3$

#### Explanation:

$D = {b}^{2} - 4 a c = 4 - 12 = - 8 < 0.$
Therefor, this function can't be factored.