Question

Factor:$6y^3-15y^2$.

Short answer

The required factor is$3y^2\left(2y-5\right)$.

Step-by-step solution

Step 1. Given information.

The given polynomial is:

$6y^3-15y^2$

Step 2. Find the GCF.

Find the GCF of $6y^3\mathrm{and}15y^2$,

$$\begin{gathered} 6y^3=2·3·y·y·y \\ 15y^2=3·5·y·y \end{gathered}$$

GCF is:

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

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$3y^2·2y-3y^2·5$

Factor the GCF,

$3y^2\left(2y-5\right)$