college Algebra constructing a polynomial (see description below)

Question

Not understanding how they are getting their answer -4x³ +32x² -84x+80

constructing a polynomial Third-degree, with zeros of 2-i,2+i, and 4, and a leading coefficient of -4

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Answer 1

If x = 4 is a root of the polynomial, then (x - 4) is a factor. Likewise, if (2 - i) is a root, then (x - (2 - i)) is a factor, as is (x - (2 + i)) since (2 + i) is also a root. Find the product of those three factors, and then multiply times -4.