Question

Factor 2x^2+ 8 or is prime?

Answer 1

Given a quadratic expression of the form

$ax^2+b$

We can factor it by:

$ax^2+b=0$

And solve for x:

$x=\pm\sqrt{-\frac{b}{a}}$

But, if we try to apply this in the given equation:

$2x^2+8=0$$\begin{gathered} 2x^2=-8 \\ . \\ x^2=-\frac{8}{2} \\ . \\ x=\pm\sqrt{-4} \end{gathered}$

Which is not a real number. Thus, the expression is prime.