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q3 - q2 + 2q - 2 = (q2+ 2)(q - 1).

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If you are prepared to enter the realm of complex numbers

(where i = √(-1) ), then

(i√2)2 = 2(i2) = -2, and

q2 + 2 = q2 - (i√2)2

= (q - i√2)(q + i√2);

and, in this case, the complete factorization is

q3 - q2 + 2q - 2 = (q2 + 2)(q - 1)

= (q - i√2)(q + i√2) (q - 1).

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13y ago

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