Question

Factor:$3y^2-12y+27$

Short answer

The required factor is$3\left(y^2-4y+9\right)$.

Step-by-step solution

Step 1. Given information.

The given polynomial is:

$3y^2-12y+27$

Step 2. Find the GCF.

Find the GCF of $3y^2,12y,\mathrm{and}27$,

$$\begin{gathered} 3y^2=3·y·y \\ 12y=2·2·3·y \\ 27=3·3·3 \end{gathered}$$

GCF$=3$

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$3·y^2-3·4y+3·9$

Factor the GCF,

$3\left(y^2-4y+9\right)$