# How do you find all the real and complex roots of f(x) = x^3 - 4x^2 - 16x + 64?

Mar 1, 2016

Use Grouping ...

#### Explanation:

$f \left(x\right) = {x}^{3} - 4 {x}^{2} - 16 x + 64$

$f \left(x\right) = \left({x}^{3} - 4 {x}^{2}\right) - \left(16 x - 64\right)$

Next, factor out common terms ...

$f \left(x\right) = {x}^{2} \left(x - 4\right) - 16 \left(x - 4\right)$

Simplify and set equal to zero ...

$f \left(x\right) = \left({x}^{2} - 16\right) \left(x - 4\right) = 0$

Solve for x ...

${x}^{2} - 16 = 0$
$x = \pm 4$

$x - 4 = 0$
$x = 4$

So, the solutions are $x = 4$ or $x = - 4$ with $x = 4$ a double root .

Hope that helped