# How do you find all the zeros of f(x) = x^3 – 10x^2 + 24x?

Aug 16, 2016

$f \left(x\right)$ has zeros $0 , 4 , 6$

#### Explanation:

$f \left(x\right) = {x}^{3} - 10 {x}^{2} + 24 x$

Since all of the terms are divisible by $x$, we can separate that out as a factor. Then we can factor the remaining quadratic using the facts that $4 + 6 = 10$ and $4 \cdot 6 = 24$...

${x}^{3} - 10 {x}^{2} + 24 x = x \left({x}^{2} - 10 x + 24\right) = x \left(x - 4\right) \left(x - 6\right)$

Hence zeros:

$x = 0$, $x = 4$ and $x = 6$.