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Question

Find a monic quadratic polynomial P(x) with integer coefficients such that P(13 - 3) = 0.(A polynomial is monic if its leading coefficient is 1.)

Accepted Answer

Let x = 13 - 3. Then x + 3 = 13, so (x + 3)^2 = 13.This simplifies to x^2 + 6x - 4 = 0, so we can take P(x) = x^2 + 6x - 4.