# How do you factor 5x^3 -10x^2 - 125x?

May 23, 2015

$5 {x}^{3} - 10 {x}^{2} - 125 x$

$= 5 x \left({x}^{2} - 2 x - 25\right)$

$= 5 x \left({x}^{2} - 2 x + 1 - 26\right)$

$= 5 x \left({\left(x - 1\right)}^{2} - {\sqrt{26}}^{2}\right)$

$= 5 x \left(x - 1 - \sqrt{26}\right) \left(x - 1 + \sqrt{26}\right)$

by completing the square and by using the identity ${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

May 23, 2015

$f \left(x\right) = 5 x \left({x}^{2} - 2 x - 25\right)$

The trinomial in parentheses can't be factored because its D = b^2 - 4ac = 4 + 100 = 104 isn't a perfect square.