c) \( \left(x^{3}-2 x+1\right)+\left(-7 x^{3}+3 x^{2}-6 x\right) \)

To simplify the expression, first combine like terms from both polynomials. Start by identifying the coefficients for each degree of \(x\): 1. For \(x^3\), combine \(x^3 - 7x^3\) to get \(-6x^3\). 2. For \(x^2\), you only have \(3x^2\). 3. For \(x\), combine \(-2x - 6x\) to get \(-8x\). 4. Finally, the constant term is \(+1\). Thus, the simplified expression is: \(-6x^3 + 3x^2 - 8x + 1\). This polynomial can now be analyzed or manipulated further as needed!