Final answer:
The division of the polynomial 3x² + 19x - 37 by x + 8 requires polynomial long division, which does not follow the same rules as division of exponentials. The rules mentioned relate to exponents and are not applicable to this polynomial division problem.
Step-by-step explanation:
The question asks us to divide the polynomial 3x² + 19x - 37 by the monomial x + 8. This process involves dividing the terms of the numerator by the divisor and finding the coefficients using polynomial long division. However, the rules given in the question are related to operations with exponential terms and are not directly applicable to polynomial division.
To divide the polynomial 3x² + 19x - 37 by x + 8, we would set up a long division problem where x + 8 is the divisor and 3x² + 19x - 37 is the dividend. We would then perform polynomial long division to find the quotient and the remainder. We cannot simplify this division with a simple rule like for division of exponentials since this is not a division of exponential terms but rather that of polynomial terms.