Final answer:
To divide the given polynomial by another polynomial, divide each term individually by dividing the coefficients and subtracting the exponents for the variables.
Step-by-step explanation:
To divide the polynomial (24x²y⁴+42x³y⁸-18x⁷y²) by (2x²y²), we can divide each term individually. Starting with the first term, 24x²y⁴, we divide the coefficients (24/2 = 12) and subtract the exponents (2-2 = 0) for the x terms, and subtract the exponents (4-2 = 2) for the y terms. This gives us 12y². We repeat this process for each term:
First term: 12y²
Second term: 21xy⁶
Third term: -9x⁵y
Therefore, the division of the polynomial by (2x²y²) is: 12y² + 21xy⁶ - 9x⁵y.