34. \( g^{3}+3 g^{2}-g-3=0 \)

Did you know that cubic equations like this one have been around for centuries? They were heavily studied by mathematicians such as Cardano in the 16th century. He developed methods to solve them that laid a foundation for modern algebra. So, tackling equations like \( g^{3}+3 g^{2}-g-3=0 \) connects you to a rich historical backdrop in mathematics! To solve this equation, consider using techniques such as synthetic division or the Rational Root Theorem. A good first step could be testing possible rational roots like \( g = 1 \) or \( g = -1 \). Once you find a root, factor the polynomial into simpler terms, making it easier to solve the remaining quadratic equation. Happy solving!