Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 18

$(z-1)(z-7)$

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}