d) \( x^{3}-x^{2}-x+1 \)

Did you know that polynomials like \( x^{3}-x^{2}-x+1 \) can be analyzed using the Intermediate Value Theorem? This means if you find values of \( x \) that give different signs when plugged into the polynomial, there exists at least one root between those \( x \) values! So, if you plug in say -1 and 1, you might discover the real zeros in an exciting way! Moreover, when looking to factor this polynomial, don't forget about synthetic division! By testing possible rational roots—like factors of the constant term—you can simplify the process. Finding one root allows you to reduce it to a quadratic, making it easier to solve. Happy factoring!