Final answer:
Long polynomial division is a method of dividing a polynomial by another polynomial of lesser or equal degree. It involves dividing the lead coefficients and subtracting the exponents term by term until the entire dividend polynomial has been divided.
Step-by-step explanation:
The question pertains to the division of polynomials using the long division method. To divide using long polynomial division, one must divide the lead terms, multiply the divisor by the result of the division, subtract the result from the dividend, and then bring down the next term. This process is repeated until all terms have been accounted for. The division of exponent terms requires you to divide the coefficients (numeric part) and subtract the exponents of the x terms. Here, we encounter a small typo in the provided polynomial; we will assume that the order of terms is corrected to -20x⁴ + 15x³ + 12x² + 5x + 9. The divisor is -5x² - 2. The long division would look complex, however, because we see that the leading term of the divisor (-5x²) has a lower degree than the leading term of the dividend (-20x⁴), implying the division could proceed as normal.