Write a polynomial with rational coefficients having roots 3,3+i, and 3-i

a. write the factors in the form (x-a) that are associated with the roots (a) given in the problem.

b. multiply the two factors with complex terms to produce a quadratic expression.

c. multiplly the quadratic expression you just found by the 1 remainder factor to find the resulting cubic polynomal

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A polynomial with roots 3, 3+i and 3-i can be written as:

(a) (x-3)(x-3-i)(x-3+i) [where each term is just x minus the root]

(b) (x-3)(x^2-3x +ix -3x+9 -3i -ix +3i +1) = (x-3)(x^2-6x+10) [where we distributed to get the product]

(c) (x-3)(x^2 - 6x +10) = x^3 -6x^2 +10x -3x^2 +18x -30 = x^3 - 9x^2 +28x -30

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