Question

factor.
$z^2 + 11z - 26$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -26 and add up to 11. Let's list the factor pairs of -26: (-1, 26), (1, -26), (-2, 13), (2, -13). Among these, 13 and -2 multiply to -26 (13 * (-2) = -26) and add up to 11 (13 + (-2) = 11).

Step2: Factor the quadratic

Using these two numbers, we can factor the quadratic \(z^2 + 11z - 26\) as \((z + 13)(z - 2)\). We check by expanding: \((z + 13)(z - 2)=z^2 - 2z + 13z - 26 = z^2 + 11z - 26\), which matches the original expression.

Answer:

\((z + 13)(z - 2)\)