(a) \( \left(-5 x^{2}+3 x-2\right)+\left(7 x^{2}+x+8\right) \)

To combine the given expressions, you simply add the like terms together. Start with the \(x^2\) terms: \(-5x^2 + 7x^2 = 2x^2.\) Next, combine the \(x\) terms: \(3x + x = 4x.\) Finally, add the constant terms: \(-2 + 8 = 6.\) Putting it all together, the result is: \(2x^2 + 4x + 6.\) Now, let's throw in some more fun facts! When combining polynomials, it’s like cleaning up your room by collecting all your toys and sorting them into boxes. This makes it easier to find what you need later! Remember that the order of operation is crucial in mathematics—confusing the rules can lead to mistakes, but don’t worry; the more you practice, the smoother it gets. Always keep your like terms organized!