The complete factorisation of the polynomial given; x³ + 2x² + 4x + 8 as in the task content can be factorised and determined as; Choice D; (x+2)(x+2i)(x-2i).
<h3>What is the complete factorisation of the given polynomial; x³ + 2x² + 4x+8?</h3>
It follows from the given task content that the polynomial whose factors are to be determined by means of factorisation is; x³ + 2x² + 4x+8.
It follows from observation that one of the zeros of the polynomial expression is at; x = -2.
Consequently, one of the factors of the polynomial in discuss is; (x+2).
x³ + 2x² + 4x+8 = (x+2) (x² - 4i²)
= (x+2)(x+2i)(x-2i)
Consequently, it follows that the complete factorisation of the polynomial is; (x+2)(x+2i)(x-2i).
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