Factor Quadratic Trinomials with Leading Coefficient 1: example 7.27

We need $r$ in the first term of each binomial and $s$ in the second term. The last term of the trinomial is negative, so the factors must have opposite signs.

$\begin{array}{cccc}& & & r^2-8rs-9s^2\hfill \\ \text{Note that the first terms are}r,\text{last terms contain}s.\hfill & & & \left(r\_s\right)\left(r\_s\right)\hfill \end{array}$

Find the numbers that multiply to $\mathrm{-9}$ and add to $\mathrm{-8}$.

$\begin{array}{cccc}\text{Use}1,\mathrm{-9}\text{as coefficients of the last terms.}\hfill & & & \hfill \left(r+s\right)\left(r-9s\right)\hfill \\ \text{Check your answer.}\hfill & & & \\ \\ \\ \left(r-9s\right)\left(r+s\right)\hfill & & & \\ r^2+rs-9rs-9s^2\hfill & & & \\ r^2-8rs-9s^2✓\hfill & & & \end{array}$