Final answer:
The question requires performing polynomial long division on (2x^3 + 7x^2 - 9) by (2x + 3) to find the quotient. Just like simplifying fractions, we divide terms until reaching a remainder with a degree lower than the denominator. The process continues step by step, similar to traditional division.
Step-by-step explanation:
The question asks to state the quotient of the expression (2x^3 + 7x^2 - 9) divided by (2x + 3). To find the quotient, we perform polynomial long division. We divide the first term of the numerator, 2x^3, by the first term of the denominator, 2x, to get x^2. We multiply x^2 by (2x + 3) and subtract that from the original numerator to find the remainder. We continue this process with the next term of the resulting polynomial until we cannot divide further due to the degree of the remainder being less than the degree of the denominator.
This process resembles how we handle simpler fractions. For instance, as we know any fraction with the same quantity in the numerator and the denominator equals 1, similarly, in polynomial division, when our remainder has cancelled down to 0, the division process is complete with no remainder left. In cases where we get a non-zero remainder, it signifies the polynomial division resulted in a quotient plus a remainder fraction, where the remainder is divided by the denominator.