Solve 2x^3-18x^2-5x+45

$$2 x ^ { 3 } - 18 x ^ { 2 } - 5 x + 45$$

Factor

$$\left(x-9\right)\left(2x^{2}-5\right)$$

Solution Steps

Do the grouping 2x^{3}-18x^{2}-5x+45=\left(2x^{3}-18x^{2}\right)+\left(-5x+45\right), and factor out 2x^{2} in the first and -5 in the second group.

$$2x^{2}\left(x-9\right)-5\left(x-9\right)$$

Factor out common term x-9 by using distributive property. Polynomial 2x^{2}-5 is not factored since it does not have any rational roots.

$$\left(x-9\right)\left(2x^{2}-5\right)$$

Evaluate

$$\left(x-9\right)\left(2x^{2}-5\right)$$