Question

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

Answer 1

`x(x-5)(4x+1)`

Explanation:

`"take out a "color(blue)"common factor "x`

`=x(4x^2-19x-5)`

`"factor the quadratic using the a-c method"`

`"the factors of the product "4xx-5=-20`

`"which sum to - 19 are - 20 and + 1"`

`"split the middle term using these factors"`

`4x^2-20x+x-5larrcolor(blue)"factor by grouping"`

`=color(red)(4x)(x-5)color(red)(+1)(x-5)`

`"take out the "color(blue)"common factor "(x-5)`

`=(x-5)(color(red)(4x+1))`

`4x^3-19x^2-5x=x(x-5)(4x+1)`