# Which is the cubic polynomial in the standard form with roots 3, -6, and 0?

Dec 4, 2016

${x}^{3} + 3 {x}^{2} - 18 x = 0$

#### Explanation:

roots are:

x=0;" "x=3;" "x=-6

hence the corresponding linear factors are:

x;" "(x-3);" "(x+6)

the cubic is them formed by their products

$x \left(x - 3\right) \left(x + 6\right) = 0$

multiply out.

$x \left({x}^{2} + 3 x - 18\right) = 0$

${x}^{3} + 3 {x}^{2} - 18 x = 0$

Dec 4, 2016

${x}^{3} + 3 {x}^{2} - 18 x$

#### Explanation:

The simplest polynomial with zeros $3$, $- 6$ and $0$ is:

$f \left(x\right) = \left(x - 3\right) \left(x + 6\right) x$

$\textcolor{w h i t e}{f \left(x\right)} = {x}^{3} + 3 {x}^{2} - 18 x$

Any polynomial in $x$ with these zeros will be a multiple (scalar or polynomial) of this $f \left(x\right)$.