Answer
$(x+1)(3x+1)$
Work Step by Step
Rearranging the terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
4x+1+3x^2
\\\\=
3x^2+4x+1
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
3x^2+4x+1
\end{array} has $ac=
3(1)=3
$ and $b=
4
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
3,1
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
3x^2+3x+1x+1
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(3x^2+3x)+(x+1)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
3x(x+1)+(x+1)
.\end{array}
Factoring the $GCF=
(x+1)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x+1)(3x+1)
.\end{array}
