How do you factor the trinomial $x^{2} + 2 x + 3$ $x^2 + 2x +3$ ?

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How do you factor the trinomial $x^{2} + 2 x + 3$ $x^2 + 2x +3$ ?

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Answer 1 · 2018-04-11T20:47:51

$(x + 1 + \sqrt{2} i) (x + 1 - \sqrt{2} i)$ $(x+1+sqrt2i)(x+1-sqrt2i)$

Explanation:

$there are no whole number factors for + 3 which sum to + 2$ $"there are no whole number factors for + 3 which sum to + 2"$

$factor using the solutions to x^{2} + 2 x + 3 = 0$ $"factor using the solutions to "x^2+2x+3=0$

$solve using the quadratic formula$ $"solve using the "color(blue)"quadratic formula"$

$with a = 1, b = 2 and c = 3$ $"with "a=1,b=2" and "c=3$

$x = \frac{- 2 \pm \sqrt{4 - 12}}{2}$ $x=(-2+-sqrt(4-12))/2$

$x = \frac{- 2 \pm \sqrt{- 8}}{2} = \frac{- 2 \pm 2 \sqrt{2} i}{2} = - 1 \pm \sqrt{2} i$ $color(white)(x)=(-2+-sqrt(-8))/2=(-2+-2sqrt2i)/2=-1+-sqrt2i$

$\Rightarrow (x - (- 1 + \sqrt{2} i)) (x - (- 1 - \sqrt{2} i))$ $rArr(x-(-1+sqrt2i))(x-(-1-sqrt2i))$

$\Rightarrow x^{2} + 2 x + 3 = (x + 1 + \sqrt{2} i) (x + 1 - \sqrt{2} i)$ $rArrx^2+2x+3=(x+1+sqrt2i)(x+1-sqrt2i)$

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How do you factor the trinomial $x^{2} + 2 x + 3$ $x^2 + 2x +3$ ?

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