Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 4, -2, and -1 + 2i

This is going to be a fourth degree polynomial because if x = 4, one of the factors is x - 4; if x = -2, then one of the factors is x + 2; and by the conjugate root theorem, if x = -1 + 2i, then -1-2i HAS to also be a root. If x = -1+2i, then the factor is (x-(-1+2i)). Simplfying that gives us (x+1-2i). Likewise, if x = -1-2i, then the factor is (x-(-1-2i)). Simplifying that gives us (x+1+2i). We will FOIL those complex factors first. Doing that we have . Once we simplify that down it's much easier to deal with than what it looks like right now. . Since i^2 = -1, what we have in the end is . Now we will multiply that by x-4. . Now finally we will multiply in the last factor of x+2. is your final fourth degree polynomial.

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