2022 SSMO Tiebreaker Round Problems/Problem 2

Problem

Let $P(x) = x^3 - 7x^2 + 9x - 2$ . If $P(x) = (x - a)^3 + b(x - a) + c$ where $a, b, c$ are real numbers, then the value of $a - b - c$ can be expressed as $\frac{m}{n}$ for relatively prime positive integers $m$ and $n$ . Find $m + n$ .

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2022 SSMO Tiebreaker Round Problems/Problem 2

Problem

Solution