Solve 5k^3-45k^2+35k-315

$$5 k ^ { 3 } - 45 k ^ { 2 } + 35 k - 315$$

Factor

$$5\left(k-9\right)\left(k^{2}+7\right)$$

Solution Steps

Factor out 5.

$$5\left(k^{3}-9k^{2}+7k-63\right)$$

Consider k^{3}-9k^{2}+7k-63. Do the grouping k^{3}-9k^{2}+7k-63=\left(k^{3}-9k^{2}\right)+\left(7k-63\right), and factor out k^{2} in the first and 7 in the second group.

$$k^{2}\left(k-9\right)+7\left(k-9\right)$$

Factor out common term k-9 by using distributive property.

$$\left(k-9\right)\left(k^{2}+7\right)$$

Rewrite the complete factored expression. Polynomial k^{2}+7 is not factored since it does not have any rational roots.

$$5\left(k-9\right)\left(k^{2}+7\right)$$

Evaluate

$$5\left(k-9\right)\left(k^{2}+7\right)$$