Solve 10n^3-2n^2-25n+5

$$10 n ^ { 3 } - 2 n ^ { 2 } - 25 n + 5$$

Factor

$$\left(5n-1\right)\left(2n^{2}-5\right)$$

Solution Steps

Do the grouping 10n^{3}-2n^{2}-25n+5=\left(10n^{3}-2n^{2}\right)+\left(-25n+5\right), and factor out 2n^{2} in the first and -5 in the second group.

$$2n^{2}\left(5n-1\right)-5\left(5n-1\right)$$

Factor out common term 5n-1 by using distributive property. Polynomial 2n^{2}-5 is not factored since it does not have any rational roots.

$$\left(5n-1\right)\left(2n^{2}-5\right)$$

Evaluate

$$\left(5n-1\right)\left(2n^{2}-5\right)$$