jmc

Question

Find a monic cubic polynomial P(x) with integer coefficients such that P([3]2 + 1) = 0.(A polynomial is monic if its leading coefficient is 1.)

Accepted Answer

Let x = [3]2 + 1. Then x - 1 = [3]2, so (x - 1)^3 = 2.This simplifies to x^3 - 3x^2 + 3x - 3 = 0. Thus, we can take P(x) = x^3 - 3x^2 + 3x - 3.