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\frac{3}{10}t^{4}+6
Divide \frac{3}{2}t^{4} by 5 to get \frac{3}{10}t^{4}.
\frac{3\left(t^{4}+20\right)}{10}
Factor out \frac{3}{10}. Polynomial t^{4}+20 is not factored since it does not have any rational roots.