SOLUTION: I am having trouble with forming polynomials using real coefficents: Degree: 4 Zeros: 4 multiplicity of 2, 2i. I have to show the final fully multiplied polynomial

The four zeros are

    x = 4,      x = 4,        x = 2i,       x = -2i   (the conjugate of 2i)

Get 0 on the right of all four:

x - 4 = 0,  x - 4 = 0,   x - 2i = 0,   x + 2i = 0

Multiply all these 4 equations:

 (x - 4)(x - 4)(x - 2i)(x + 2i) = 0

Multiply the first two together:

                (x - 4)(x - 4) = x² - 4x - 4x + 16 = x² - 8x + 16


Multiply the last two together:

                (x - 2i)(x + 2i) = x² + 2ix - 2ix + 4i² = x² - 4i² = 
                                 = x² - 4(-1) = x² + 4

Now multiply those together

(x² - 8x + 16)(x² + 4) = 0

Then we have:

x⁴ - 8x³ + 16x² + 4x² - 32x + 64 = 0

      x⁴ - 8x³ + 20x² - 32x + 64 = 0

Edwin