Question

In the following exercises, factor completely.

$48q^3-24q^2+3q$

Short answer

The simplified expression is$3q{(4q-1)}^2$

Step-by-step solution

Step 1. Given Information 

The given expression is$48q^3-24q^2+3q$

Step 2. Calculation 

We will find the factor of polynomial by using perfect square trinomial pattern,

$$\begin{gathered} 48q^3-24q^2+3q=3q(16q^2-8q+1) \\ =3q({\left(4q\right)}^2-2\times 4q\times 1+{\left(1\right)}^2) \\ =3q{(4q-1)}^2 \end{gathered}$$