Factor Quadratic Trinomials with Leading Coefficient 1: example 7.21

To get a negative last term, multiply one positive and one negative. We need factors of $\mathrm{-5}$ that add to positive 4.

Notice: We listed both $1,\mathrm{-5}\text{and}-1,5$ to make sure we got the sign of the middle term correct.

$\begin{array}{cccc}& & & z^2+4z-5\hfill \\ \text{Factors will be two binomials with first terms}z.\hfill & & & \left(z\right)\left(z\right)\hfill \\ \text{Use}\mathrm{-1},5\text{as the last terms of the binomials.}\hfill & & & \left(z-1\right)\left(z+5\right)\hfill \\ \text{Check.}\hfill & & & \\ \\ \\ \left(z-1\right)\left(z+5\right)\hfill & & & \\ z^2+5z-1z-5\hfill & & & \\ z^2+4z-5✓\hfill & & & \end{array}$