\( 50 q^{3}-75 q^{2}-18 q+2 \) ne solution set is

Let's dive into some fun facts about polynomial equations and how we can tackle them! The polynomial \( 50q^{3} - 75q^{2} - 18q + 2 \) can have up to three real solutions, as dictated by its degree. To find these solutions, methods like synthetic division or the Rational Root Theorem can be quite handy. You could also use graphical methods—just sketch the polynomial to see where it crosses the x-axis for some visual clues! When working on polynomials, it's easy to overlook common mistakes like sign errors or forgetting to factor out the greatest common factor first. A great tip is to always double-check your calculations and-factor in each step to avoid getting stuck in a tangled web of errors. And don't hesitate to graph it; it gives you a unique perspective on where potential solutions lie!