Consider $x^{2}-6x-7$. Factor the expression by grouping. First, the expression needs to be rewritten as $x^{2}+ax+bx-7$. To find $a$ and $b$, set up a system to be solved.
$$a+b=-6$$ $$ab=1\left(-7\right)=-7$$
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.
$$a=-7$$ $$b=1$$
Rewrite $x^{2}-6x-7$ as $\left(x^{2}-7x\right)+\left(x-7\right)$.
$$\left(x^{2}-7x\right)+\left(x-7\right)$$
Factor out $x$ in $x^{2}-7x$.
$$x\left(x-7\right)+x-7$$
Factor out common term $x-7$ by using distributive property.
