Question

What of the following is the complete factorization of the polynomial - x^3+2x^2+x+2

A.(x+2)(x+i)(x-i)
B. (x-2)(x+i)(x-i)
C. (x-2)(x+i)(x+i)
D. (x+2)(x+i)(x+i)

Answer 1

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Answer:

A. (x +2)(x +i)(x -i)

Explanation:

The complex factors must be conjugates, eliminating choices C and D.

The product of the complex factors will be (x^2 +1) so the remaining factor must have a constant of +2 in order for the constant in the product to be 2.

p(x) = (x +2)(x² +1) = (x +2)(x +i)(x -i)