Final answer:
The division of the given polynomial by a binomial is solved using polynomial long division, which involves repeated processes of division, multiplication, and subtraction until the remainder has a lesser degree than the denominator.
Step-by-step explanation:
The student's question pertains to dividing a polynomial by a binomial, specifically (x^3 + 3x^2 - 4x - 6) ÷ (x^2 - 4). This process is known as polynomial long division, which is somewhat analogous to long division with numbers. To perform the division, you would first look at the leading term of the numerator (x^3) and the leading term of the denominator (x^2) and divide these to determine the first term of the quotient (x). Multiplying the entire denominator by this new term and subtracting it from the original numerator gives a new remainder.
Continue this process of dividing, multiplying, and subtracting until the remainder has a degree less than the denominator or is zero. Since the given polynomial division does not immediately suggest any form of simplification, such as factoring or canceling common terms, we must use polynomial long division straight away to reach the answer.