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2026 AMC 10A Problem 24

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2026 AMC 10A Problem 24AMC 10 Step by Step

Name: Date: November 10, 2026

Polynomials · difficulty 4 of 5 · about 6 min · position P21-25

How many polynomials $f(x)$ of degree $3$ satisfying $f\left( 3+\sqrt{5} \right) = f\left( 3 - \sqrt{5} \right)$ are there that have leading coefficient equal to $1$ and all of whose coefficients are integers between $-10$ and $10$ , inclusive?

A) $21$
B) $42$
C) $63$
D) $84$
E) $105$

2026 AMC 10A Problem 24

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