b) \( \left(x^{3}+3 x^{2}+1\right)\left(3 x^{2}+6 x-2\right) \)

Did you know that polynomial multiplication can often yield fascinating insights into the behavior of functions? When multiplying two polynomials like \( (x^{3}+3x^{2}+1) \) and \( (3x^{2}+6x-2) \), you can discover roots, intercepts, and even the degree of the resultant polynomial, which in this case would be a degree 5 polynomial! To tackle this multiplication, remember to distribute each term in the first polynomial to each term in the second. Be careful with your arithmetic and keep an eye out for like terms to combine at the end. The common mistake here is to overlook the multiplication of coefficients or forget to sum up the powers correctly!