\(3m^2-2m-1\)
\(=3m^2-3m+m-1\)
\(=3m\left(m-1\right)+\left(m-1\right)\)
\(=\left(m-1\right)\left(3m+1\right)\)
\(3m^2-2m-1\)
\(=3m^2+m-3m-1\)
\(=\left(3m^2+m\right)-\left(3m+1\right)\)
\(=m\left(3m+1\right)-\left(3m+1\right)\)
\(=\left(m-1\right)\left(3m+1\right)\)