Question

In the following exercises, factor completely.

$3x^3-36x^2+108x$

Short answer

On factoring, we get $3x{\left(x-6\right)}^2$.

Step-by-step solution

Step 1. Given information.

Consider the given question,

$3x^3-36x^2+108x$

Factor out the GCF,

$=3x\left(x^2-12x+36\right)$

On simplifying the expression,

role="math" localid="1644848929090" $$\begin{gathered} =3x\left(x^2-6x-6x+36\right) \\ =3x\{x\left(x-6\right)-6\left(x-6\right)\} \\ =3x{\left(x-6\right)}^2 \end{gathered}$$

Step 2. Check the answers.

Check by multiplying,

$$\begin{gathered} =3x{\left(x-6\right)}^2 \\ =3x\left(x^2+36-12x\right) \\ =3x^3+108x-36x^2 \end{gathered}$$