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

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

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Answer 1 · 2015-05-08T23:21:01

$x^{2} + x + 2$ $x^2 + x + 2$ is not factorable using rational numbers. This means that no rational numbers added together equal $1$ $1$ ( $x$ $x$ in equation) and multiplied together equal $2$ $2$ .

You can find the imaginary answer to $x^{2} + x + 2 = 0$ $x^2 + x + 2 = 0$ (an equation, notice the $=$ $=$ ), however.

Using the quadratic formula: $\frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $(-b+-sqrt(b^2-4ac))/(2a)$

$x$ $x$ would then equal $\frac{- 1 \pm i \sqrt{7}}{2}$ $(-1 +- isqrt(7))/2$

and the factors would be
$x^{2} + x + 2 = (x + \frac{1 + \sqrt{7} i}{2}) (x + \frac{1 - \sqrt{7} i}{2})$ $x^2+x+2 = (x+(1+sqrt(7)i)/2)(x+(1-sqrt(7)i)/2)$

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

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