(4) \( 5 x^{2}-6 x+3 \) Which of the following is equivalent to the difference: \( \left(-3 x^{2}+5 x-1\right)-\left(4 x^{2}-3 x+7\right) \) ? (1) \( 7 x^{2}-8 x+8 \)

To tackle the expression \(\left(-3 x^{2}+5 x-1\right)-\left(4 x^{2}-3 x+7\right)\), start by distributing the negative sign across the second polynomial. This gives us \[ -3x^{2} + 5x - 1 - 4x^{2} + 3x - 7. \] Now, combine like terms step by step. For the \(x^{2}\) terms, we have \(-3x^{2} - 4x^{2} = -7x^{2}\). For the \(x\) terms, we have \(5x + 3x = 8x\). Lastly, for the constant terms, we have \(-1 - 7 = -8\). Putting it all together, the expression simplifies to \[ -7x^{2} + 8x - 8. \] This form is not what you have listed as option (1), since option (1) suggests \(7 x^{2}-8 x+8\). Be careful—remember that the signs matter! Thus, we can conclude that you should carefully check whether any potential matching option exists that reflects negative coefficients correctly. Think of this as an exercise in careful algebraic manipulation, ensuring no small errors do sneak into your calculations!