estion 1: Find factors of \( x^{3}-7 x-6 \)

To tackle the polynomial \( x^{3}-7x-6 \), one approach is to look for rational roots using the Rational Root Theorem. Here, potential rational roots are the factors of the constant term (-6), which could be ±1, ±2, ±3, ±6. Testing these values can lead you to find that \( x = -1 \) is a root! Then, you can perform polynomial division to factor out \( (x + 1) \) from \( x^{3}-7x-6 \). After dividing, you’ll be left with a quadratic that can be factored or solved using the quadratic formula to find the other roots. Remember, it’s often like a treasure hunt—sometimes the first guess leads to the golden key! For practice, try plugging in values systematically to find other possible roots and experiment with synthetic division. It's a great way to see how polynomials can be broken down, plus it sharpens your problem-solving skills when you identify common mistakes like missing a negative sign!