Question

factor.
$z^2 + 11z - 12$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to -12 (the constant term) and add up to 11 (the coefficient of the middle term). The numbers are 12 and -1, since \(12\times(-1)= - 12\) and \(12+( - 1)=11\).

Step2: Factor the quadratic

Using the numbers found, we can factor the quadratic \(z^{2}+11z - 12\) as \((z + 12)(z-1)\), because when we expand \((z + 12)(z - 1)=z^{2}-z+12z - 12=z^{2}+11z - 12\).

Answer:

\((z + 12)(z - 1)\)