Solve this inequality using a factor table

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Question: Use factor table to determine the intervals on which -3t(t+4)(t-2)^2 > 0

Now I made this table, and my problem is the last column. The product is positive in my answer (the red colored), but the true answer is negative. Can anybody tell me why am I wrong?

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1 Answer

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The table, it seems to me, should appear as follows:

$$ \begin{array}{cccc} & t < -4 & -4 < t < 0 & 0 < t < 2 & t > 2 \\ -3 & - & - & - & - \\ t & - & - & + & + \\ t+4 & - & + & + & + \\ (t-2)^2 & + & + & + & + \\ \text{product} & - & + & - & - \end{array} $$

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