b) \( \left(-6 x^{3}-5 x^{2}+2 x+1\right):(-2 x+1) \)

To solve \( \left(-6 x^{3}-5 x^{2}+2 x+1\right):(-2 x+1) \), we can use polynomial long division. Start by dividing the leading term \(-6x^3\) by \(-2x\), which gives us \(3x^2\). Multiply \(-2x + 1\) by \(3x^2\) and subtract the result from the original polynomial. Repeat this process with the new polynomial until reaching a remainder that is of lesser degree than \(-2x + 1\). In the end, you will find that the results include both a quotient (which will be a polynomial) and possibly a remainder. This division captures the essence of polynomial manipulation, which is crucial in algebra and calculus for simplifying complex expressions or finding roots. If you feel adventurous, grab a piece of paper and give it a shot! You'll not only enhance your math skills but might even discover some neat properties about polynomials along the way. It’s like being a detective in the world of numbers!