Consider $3x^{2}-2x-1$. Factor the expression by grouping. First, the expression needs to be rewritten as $3x^{2}+ax+bx-1$. To find $a$ and $b$, set up a system to be solved.
$$a+b=-2$$ $$ab=3\left(-1\right)=-3$$
Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.
$$a=-3$$ $$b=1$$
Rewrite $3x^{2}-2x-1$ as $\left(3x^{2}-3x\right)+\left(x-1\right)$.
$$\left(3x^{2}-3x\right)+\left(x-1\right)$$
Factor out $3x$ in $3x^{2}-3x$.
$$3x\left(x-1\right)+x-1$$
Factor out common term $x-1$ by using distributive property.
