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5\left(21n^{3}+35n^{2}-15n-25\right)
Factor out 5.
\left(3n+5\right)\left(7n^{2}-5\right)
Consider 21n^{3}+35n^{2}-15n-25. By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -25 and q divides the leading coefficient 21. One such root is -\frac{5}{3}. Factor the polynomial by dividing it by 3n+5.
5\left(3n+5\right)\left(7n^{2}-5\right)
Rewrite the complete factored expression. Polynomial 7n^{2}-5 is not factored since it does not have any rational roots.