Question

factor.
$z^2 - 8z - 20$

Explanation:

Step1: Find pair of factors of -20

We need two numbers that multiply to $-20$ and add to $-8$. These numbers are $-10$ and $2$, since $(-10) \times 2 = -20$ and $(-10) + 2 = -8$.

Step2: Split middle term and factor

Rewrite the quadratic by splitting the middle term, then factor by grouping:

$$\begin{align*} z^2 - 8z - 20 &= z^2 -10z + 2z -20 \\ &= z(z-10) + 2(z-10) \\ &= (z-10)(z+2) \end{align*}$$

Answer:

$(z-10)(z+2)$