Subtract the polynomials: \( (5x^{2} + 3x - 7) - (2x^{2} - x + 4) \)

To subtract the polynomials, we distribute the minus sign across the second polynomial and then combine like terms. Start with the given expression: \[ (5x^{2} + 3x - 7) - (2x^{2} - x + 4) \] Distributing the minus sign gives us: \[ 5x^{2} + 3x - 7 - 2x^{2} + x - 4 \] Now, combine like terms: 1. For the \(x^2\) terms: \(5x^2 - 2x^2 = 3x^2\) 2. For the \(x\) terms: \(3x + x = 4x\) 3. For the constant terms: \(-7 - 4 = -11\) Putting it all together, we have: \[ 3x^{2} + 4x - 11 \] So, the result of subtracting the polynomials is: \[ 3x^{2} + 4x - 11 \]