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How many choices? (Posted on 2019-02-05) Difficulty: 3 of 5
Polynomial p(x) has integer coefficients and p(3)=−2.

For what values n may it be possible for (x-n) to be a factor of p(x)?

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  Submitted by Brian Smith    
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Solution: (Hide)
armando has his solution here. Mine is below.

Let q(x) be the polynomial resulting from translating p(x) 3 units to the left on the x axis. Then q(x) = p(x+3) and p(3)=-2 implies q(0)=-2.

The possible roots of q(x) are then the signed factors of -2: -2, -1, 1, and 2. Reversing the translation then means that 1, 2, 4, and 5 are the possible roots of p(x).

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  Subject Author Date
Solutionarmando2019-02-10 03:30:51
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