Question

Find the missing factor.5s^2+ 23s + 24 = (5s + 8)( ? )

Answer 1

The missing factor is found as follows:

- we have to find two monomials that, when multiplied together, gives:

$5s^2\times24=120s^2$

and, when added together gives:

$23s$

Now, such two monomials are: 15s and 8s

since:

$15s\times8s=120s^2$

and:

$15s+8s=23s$

Therefore, we can rewrite the left-hand side of the equation as:

$\begin{gathered} 5s^2+(23s)+24 \\ \Rightarrow5s^2+(8s+15s)+24 \end{gathered}$

We can now find the missing factor by factorization, as follows:

$\begin{gathered} 5s^2+8s+15s+24 \\ \Rightarrow s(5s^{}+8)+3(5s+8) \\ \Rightarrow(5s+8)(s+3) \end{gathered}$

Therefore, the missing factor is: (s + 3)