# How do you factor 4x^3 - 19x^2 - 5x?

May 25, 2018

$x \left(x - 5\right) \left(4 x + 1\right)$

#### Explanation:

$\text{take out a "color(blue)"common factor } x$

$= x \left(4 {x}^{2} - 19 x - 5\right)$

$\text{factor the quadratic using the a-c method}$

$\text{the factors of the product } 4 \times - 5 = - 20$

$\text{which sum to - 19 are - 20 and + 1}$

$\text{split the middle term using these factors}$

$4 {x}^{2} - 20 x + x - 5 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$= \textcolor{red}{4 x} \left(x - 5\right) \textcolor{red}{+ 1} \left(x - 5\right)$

$\text{take out the "color(blue)"common factor } \left(x - 5\right)$

$= \left(x - 5\right) \left(\textcolor{red}{4 x + 1}\right)$

$4 {x}^{3} - 19 {x}^{2} - 5 x = x \left(x - 5\right) \left(4 x + 1\right)$