# How do you factor f(x)=x^3-4x^2-25x+100?

Jun 13, 2015

${x}^{3} - 4 {x}^{2} - 25 x + 100 = \left(x + 5\right) \left(x - 5\right) \left(x - 4\right)$

#### Explanation:

Start by factoring by grouping:
${x}^{3} - 4 {x}^{2} - 25 x + 100 = \left({x}^{3} - 4 {x}^{2}\right) + \left(- 25 x + 100\right)$

$= {x}^{2} \left(x - 4\right) - 25 \left(x - 4\right)$

$= \left({x}^{2} - 25\right) \left(x - 4\right)$

Now we see that ${x}^{2} - 25$ is a difference of squares, so we can factor it too.

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