Final answer:
The quotient of (3x² + 8x - 3) ÷ (x³) is 3/x + 8/x² - 3/x³.
Step-by-step explanation:
To divide the polynomial (3x² + 8x - 3) by the monomial x³, we can rewrite the expression as (3x² + 8x - 3) ÷ (x³) = 3x²/x³ + 8x/x³ - 3/x³. Using the rule for dividing variables with exponents, we subtract the exponents of x: 3x²/x³ = 3x^2-3 = 3/x. So the quotient is 3/x + 8/x² - 3/x³. Therefore, the correct answer is Option A: 3x + 8/x² - 3/x³.