Final answer:
To divide the given polynomial by (6x + 3), divide the leading terms and subtract the exponents, similar to the division of exponentials where coefficients are divided and exponents subtracted. Continue this process until you can no longer divide terms.
Step-by-step explanation:
Polynomial Long Division
Dividing the polynomial (24x³ - 12x² + 6x + 4) by (6x + 3) involves a process similar to long division with numbers. The first step is to divide the leading term of the numerator by the leading term of the denominator. Here, we divide 24x³ by 6x obtaining 4x² as the first term of the quotient. Multiplying the divisor by 4x² and subtracting this product from our polynomial, we continue this process until we reach a remainder that is less than the degree of the divisor or until we have a zero remainder.
As for the Division of Exponentials, an unrelated concept, you divide the coefficients and subtract the exponents of like bases. For instance, 10⁶ ÷ 10³ = 10³ since 6 - 3 = 3.