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2023 AMC 10B Problem 12

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2023 AMC 10B Problem 12AMC 10 Step by Step
Name:                             Date: September 13, 2026
Polynomials · difficulty 3 of 5 · about 3 min · position P11-15

When the roots of the polynomial

P(x)=(x−1)1(x−2)2(x−3)3⋅⋅⋅(x−10)10P(x) = (x-1)^1 (x-2)^2 (x-3)^3 \cdot \cdot \cdot (x-10)^{10}

are removed from the number line, what remains is the union of 1111 disjoint open intervals. On how many of these intervals is P(x)P(x) positive?

  1. A)

    33

  2. B)

    77

  3. C)

    66

  4. D)

    44

  5. E)

    55

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