2023 AMC 10 A

Complete problem set with solutions and individual problem pages

Problem 21 Medium

Let P(x) be the unique polynomial of minimal degree with the following properties:

·P(x) has leading coefficient 1.

·1 is a root of P(x) - 1.

·2 is a root of P(x-2),

·3 is a root of P(3x), and

·4 is a root of 4P(x).

The roots of P(x) are integers, with one exception. The root that is not an integer can be written as \frac { m } { n }, where m and n are relatively prime positive integers. What is m + n?

  • A.

    41

  • B.

    43

  • C.

    45

  • D.

    47

  • E.

    49

Answer:C
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