## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$(z-1)(z-7)$
The 2 numbers whose product is $ac= 1(7)=7$ and whose sum is $b= -8$ are $\left\{ -1,-7 \right\}.$ Using these two numbers to decompose the middle term of the given trinomial, $z^2-8z+7 ,$ then the factored form is \begin{array}{l} z^2-1z-7z+7 \\\\= (z^2-1z)-(7z-7) \\\\= z(z-1)-7(z-1) \\\\= (z-1)(z-7) .\end{array}