Since the coeffcients are real, and 3+i is a solution, so is its conjugate 3-i Start with x=-2, x=4, x=3+i, x=3-i x+2=0, x-4=0, x-3-i=0 x-3+i=0 Multiply all the left sides and all the right sides, which gives (x+2)(x-4)(x-3-i)(x-3+i) = 0 Do all that multiplying remembering that i2 = -1 and get x4-8x3+14x2+28x-80 = 0 So the polynomial function f(x) is f(x) = x4-8x3+14x2+28x-80 Edwin