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What this means, I believe, is that the function has zero value when the variable x is -1, 3 or 4. The polynomial must therefore contain the factors (x+1), (x-3) and (x-4). To find the function, f(x), we multiply these factors together. First multiply the first two factors to give x^2-2x-3, then multiply by the third factor, x^3-2x^2-3x-4x^2+8x+12. Gather similar terms together and we get x^3-6x^2+5x+12. Check the answer by substituting the three values of x for which f(x)=0.

Other polynomials are possible. The answer given is the simplest. By multiplying the function by a constant and/or repeats of the discovered factors, more polynomials can be created with the same number of zeroes.

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