Factor \( (b-2)\left(b^{2}+3\right) \)

To factor the expression \( (b-2)\left(b^{2}+3\right) \), we first notice that \( b-2 \) is already a linear term, and \( b^{2}+3 \) is a sum of squares, which cannot be factored over the real numbers. So, the expression is already in its simplest factored form as \( (b-2)(b^{2}+3) \). Now, let's express it as a product once again: \( (b-2)(b^2 + 3) \), highlighting how \( b^2 + 3 \) can also represent an idea rather than just a term—think of it as a 'stable base' that can’t be broken down further in fields of real numbers, making \( (b-2) \) stand out as the intriguing part of the expression! We also observe that if you were to expand it back out, you'd return to \( b^3 - 2b^2 + 3b - 6 \). While this might seem like a roundabout way of reinforcing our original factors, it's a great reminder that factoring and expanding are two sides of the same mathematical coin!