Question

factor completely.
$z^2 + 12z - 13$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-13\) and add up to \(12\). The numbers are \(13\) and \(-1\) since \(13\times(-1)= -13\) and \(13 + (-1)=12\).

Step2: Factor the quadratic

Using the numbers from Step 1, we can factor \(z^{2}+12z - 13\) as \((z + 13)(z - 1)\).

Answer:

\((z + 13)(z - 1)\)