Factor polynomial \( b^{3}-2 b^{2}+3 b-6 \)

To factor the polynomial \( b^{3}-2 b^{2}+3 b-6 \), we can apply the Rational Root Theorem. Testing possible rational roots, we find that \( b=2 \) works. Performing synthetic division with \( b-2 \), we reduce the polynomial to \( (b-2)(b^{2}+3) \). The result indicates that our polynomial factors into \( (b-2)(b^{2}+3) \). However, since \( b^2 + 3 \) doesn't factor further with real numbers, we can also express the factorization over the complex numbers as \( (b-2)(b+i\sqrt{3})(b-i\sqrt{3}) \). Voilà! And there you have it!