Evaluate
\frac{\sqrt{15}\left(x^{2}+8\right)}{15}
Factor
\frac{\sqrt{15}\left(x^{2}+8\right)}{15}
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\frac{8+x^{2}}{\sqrt{15}}
Add 3 and 5 to get 8.
\frac{\left(8+x^{2}\right)\sqrt{15}}{\left(\sqrt{15}\right)^{2}}
Rationalize the denominator of \frac{8+x^{2}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.
\frac{\left(8+x^{2}\right)\sqrt{15}}{15}
The square of \sqrt{15} is 15.
\frac{8\sqrt{15}+x^{2}\sqrt{15}}{15}
Use the distributive property to multiply 8+x^{2} by \sqrt{15}.
factor(\frac{8+x^{2}}{\sqrt{15}})
Add 3 and 5 to get 8.
factor(\frac{\left(8+x^{2}\right)\sqrt{15}}{\left(\sqrt{15}\right)^{2}})
Rationalize the denominator of \frac{8+x^{2}}{\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.
factor(\frac{\left(8+x^{2}\right)\sqrt{15}}{15})
The square of \sqrt{15} is 15.
factor(\frac{8\sqrt{15}+x^{2}\sqrt{15}}{15})
Use the distributive property to multiply 8+x^{2} by \sqrt{15}.
\sqrt{15}\left(8+x^{2}\right)
Consider 8\sqrt{15}+x^{2}\sqrt{15}. Factor out \sqrt{15}.
\frac{\left(8+x^{2}\right)\sqrt{15}}{15}
Rewrite the complete factored expression. Polynomial 8+x^{2} is not factored since it does not have any rational roots.
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