Question

Factor:$3p^3-6p^{2}q+9p{q}^3$.

Short answer

The required factor is$3p\left(p^2-2pq+3q^2\right)$.

Step-by-step solution

Step 1. Given information.

The given polynomial is:

$3p^3-6p^{2}q+9p{q}^3$

Step 2. Find the GCF.

Find the GCF of $3p^3,6p^{2}q,\mathrm{and}9p{q}^3$,

$$\begin{gathered} 3p^3=3·p·p·p \\ 6p^{2}q=2·3·p·p·q \\ 9p{q}^3=3·3·p·q·q·q \end{gathered}$$

GCF$=3p$

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$3p·p^2-3p·2pq+3p·3q^2$

Factor the GCF,

$3p\left(p^2-2pq+3q^2\right)$