Q. 224 - Intermediate Algebra

Question

In the following exercises, factor completely.  

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

Step-by-Step Solution

Answer

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

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,

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