What is the product? \( \left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right) ? \) \( 12 x^{9}+15 x^{8}-8 x^{6}-10 x^{5} \) \( 12 x^{24}+15 x^{12}-8 x^{8}-10 x^{4} \) \( 12 x^{9}-10 x^{5} \) \( 12 x^{24}-10 x^{4} \)

To find the product of \( \left(x^{4}\right)\left(3 x^{3}-2\right)\left(4 x^{2}+5 x\right) \), you can distribute step-by-step. Start by multiplying \( x^{4} \) with each term inside the parentheses of \( (3 x^{3}-2) \) and \( (4 x^{2}+5 x) \). After computing, collect like terms to simplify your expression. Upon carrying out the multiplication correctly, you will arrive at \( 12 x^{9}+15 x^{8}-8 x^{6}-10 x^{5} \). The key part here is to be systematic in distributing each term to avoid missing any products, as they contribute to the final polynomial!