Factor Quadratic Trinomials with Leading Coefficient 1: example 7.18

Notice that the variable is u, so the factors will have first terms u.

$\begin{array}{cccc}& & & u^2+11u+24\hfill \\ \text{Write the factors as two binomials with first terms}u.\hfill & & & \left(u\right)\left(u\right)\hfill \end{array}$

Find two numbers that: multiply to 24 and add to 11.

$\begin{array}{cccc}\text{Use 3 and 8 as the last terms of the binomials.}\hfill & & & \hfill \left(u+3\right)\left(u+8\right)\hfill \\ \\ \text{Check.}\hfill & & & \\ \\ \\ \left(u+3\right)\left(u+8\right)\hfill & & & \\ u^2+3u+8u+24\hfill & & & \\ u^2+11u+24✓\hfill & & & \end{array}$