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\frac{2\left(ax^{2}+2a\right)}{5}
Factor out \frac{2}{5}.
a\left(x^{2}+2\right)
Consider ax^{2}+2a. Factor out a.
\frac{2a\left(x^{2}+2\right)}{5}
Rewrite the complete factored expression. Polynomial x^{2}+2 is not factored since it does not have any rational roots.