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

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SOLUTION

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)

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