\( (x-6)\left(x^{2}+4 x\right) \) A. \( x^{3}-2 x^{2}-24 x \) B. \( x^{3}-10 x^{2}-24 x \) C. \( x^{3}-2 x^{2}-24 \) D. \( x^{3}-10 x^{2}-24 \)

To simplify \( (x-6)\left(x^2 + 4x\right) \), start by distributing \( (x-6) \) over \( (x^2 + 4x) \). 1. Multiply \( x \) with both terms: \( x \cdot x^2 + x \cdot 4x = x^3 + 4x^2 \). 2. Then multiply \( -6 \) with both terms: \( -6 \cdot x^2 - 6 \cdot 4x = -6x^2 - 24x \). 3. Combine the results: \( x^3 + 4x^2 - 6x^2 - 24x = x^3 - 2x^2 - 24x \). So the answer is A. \( x^3 - 2x^2 - 24x \). When it comes to polynomial multiplication, one common pitfall is forgetting to distribute each term correctly or omitting the negative signs. Double-checking each step ensures that you capture every component accurately, leading to the correct final expression.