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MathNet 2019-part-08 — 179 problems (EN–VI) Question 59

Math Olympiad Vault · MathNet 2019-part-08 — 179 problems (EN–VI)

Question 59

A polynomial $P$ with integer coefficients is called tricky if it has $4$ as a root.
A polynomial is called teeny if it has degree at most $1$ and integer coefficients between $-7$ and $7$, inclusive.
How many nonzero tricky teeny polynomials are there?