Suppose p(x) is a polynomial of degree 7 such that is a factor of p(x) + 1 and is a factor of p(x) - 1. Find p(x).
(Source: Trinity University Mathematics POTW)
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Hint: Spoiler: where Q(x) is a polynomial of degree 3.
What can you say about the derivative of p(x)?
To get you started, write the formulas for what the two statements mean.
p(x) + 1 = ...
P(x) - 1 = ...
Here's a solution assuming the polynomial is over the reals (or the complex field); by the way, good hint. Spoiler:
Thanks and congratulations to Ishuda and particularly johng for their efforts. No need to post my solution this week as johng's post is virtually identical to mine.
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