Seeing that the last (the constant) term is -3, we could make the reasonable assumption that one of the zeros of this function may be among {-3, -1, 1, 3}. Choosing any one of these possible zeros, we can do synthetic division to determine whethere or not the chosen number actually is a zero of this function.
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-1 / 1 -2 -3 -3
-1 3 0
------------------------
1 -3 0 -3 Since there is a non-zero remainder, we know
that -1 is NOT a zero.
Is -3 a zero? Let's try it:
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-3 / 1 -2 -3 -3
-3 15 -39
------------------------
1 -5 13 -42 No, -3 is not a zero, because the remainder is
not zero.
At this point I ask you to double check to ensure that you have copied this problem down correctly. I graphed this function on my TI-83 calculator and have found that there is only one real root, and that root is not an integer.
