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 \(26\): \(1\) and \(26\), \(2\) and \(13\). Since the product is negative, one number is positive and the other is negative. We want the sum to be positive \(11\), so the larger number should be positive. So we take \(13\) and \(-2\) because \(13\times(-2)= -26\) and \(13 + (-2)=11\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(z^{2}+11z - 26\) as \((z + 13)(z-2)\) because when we expand \((z + 13)(z - 2)=z^{2}-2z+13z - 26=z^{2}+11z - 26\).

Answer:

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