The polynomial function f(x) = x³ - 6x² - 8x
<h3>How to write the polynomial function?</h3>
To find a polynomial function f(x) of least degree having only real coefficients with zeros of 0, 2i, and 3+i, its factors are x, x - 2i and x - (3 + i)
So f(x) is the product of the factors
f(x) = x(x - 2i)[x - (3 + i)]
= (x² - 2ix)[x - (3 + i)]
= x³ - x²(3 + i) - 2ix² - 2ix × (-[3 + i])]
= x³ - 3x² - x²i - 2ix² - 2ix × (-[3 + i])]
= x³ - 3x² - x²i - 2ix² - 6ix + 2i²x
= x³ - 3x² - x²i - 2ix² - 6ix + 2i²x
= x³ - 3x² - x²i - 2ix² - 6ix - 2x
= x³ - 3x² - x²i × -i - 2ix² × -i - 6ix × -i - 2x
= x³ - 3x² - x²i × -i - 2(-i²)x² - 6(-i²)x - 2x
= x³ - 3x² - x² - 2x² - 6x - 2x
= x³ - 3x² - 3x² - 8x
= x³ - 6x² - 8x
So, the polynomial function f(x) = x³ - 6x² - 8x
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