\begin{tabular}{r}\( 6 x^{2}-5 x+3 \) \\ \( -\quad\left(3 x^{2}+8 x-4\right) \) \\ \hline A \( 3 x^{2}+13 x-1 \) \\ B. \( 3 x^{2}-3 x+7 \) \\ C. \( 3 x^{2}+3 x-1 \) \\ D. \( 3 x^{2}-13 x+7 \)\end{tabular}

To solve the expression \( 6x^2 - 5x + 3 - (3x^2 + 8x - 4) \), we start by distributing the negative sign across the second polynomial. This gives us: \[ 6x^2 - 5x + 3 - 3x^2 - 8x + 4 \] Next, we combine like terms: - For \(x^2\) terms: \(6x^2 - 3x^2 = 3x^2\) - For \(x\) terms: \(-5x - 8x = -13x\) - For constant terms: \(3 + 4 = 7\) Putting it all together, we have: \[ 3x^2 - 13x + 7 \] So the correct option is D: \(3x^2 - 13x + 7\). The journey of combining polynomials is like a dance! You remove the negative sign like lifting a curtain to reveal the hidden beauty of your equation, then seamlessly pair the partners (like terms) for a grand finish. Just remember, every term needs to find its match to create harmony in your final expression! When tackling similar problems in the future, double-checking your signs works wonders! Forgetting a negative can lead you down a confusing path, much like misreading a treasure map. Always take a moment to simplify step by step, so you don’t end up lost in your calculations!