Answer
$(3x+4)(x-1)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
3x^2+x-4
\end{array} has $ac=
3(-4)=-12
$ and $b=
1
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
4,-3
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
3x^2+4x-3x-4
.\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+4x)-(3x+4)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
x(3x+4)-(3x+4)
.\end{array}
Factoring the $GCF=
(3x+4)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(3x+4)(x-1)
.\end{array}