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- Thread starter judytl3
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- Jan 26, 2012

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Set $x^{2}+12x+k=(x+a)(x+b)=x^{2}+(a+b)x+k.$

Evidently, then, the values of $k$ are products of numbers whose sum is $12$. The possibilities are as follows:

\begin{align*}

1+11=12& \to k=11\\

2+10=12& \to k=20\\

3+9=12& \to k=27\\

4+8=12& \to k=32\\

5+7=12& \to k=35\\

6+6=12& \to k=36.

\end{align*}

Then they repeat.