Question

Factor the polynomial: s^2+ 12s + 32

Answer 1

We want to factor the polynomial

`s^2+12s+32`

To do this we look for two values with s such that when we multiply them, we get 32 and when we add then we get the middle item 12s.

These are 8s and 4s because

`\begin{gathered} 8s+4s=12s \\ 8s*4s=32s^2 \end{gathered}`

Now we replace 8s and 4s with the middle item and factorize, we have

`\begin{gathered} s^2+12s+32 \\ s^2+8s+4s+32 \\ s(s+8)+4(s+8) \\ (s+4)(s+8) \end{gathered}`

Hence the answer is

(s + 4) (s + 8)