Final answer:
To divide the polynomial 18n^2 + 75n + 29 by n + 4 using long division, follow the steps of long division and simplify the expression.
Step-by-step explanation:
In this question, we are asked to divide the polynomial 18n^2 + 75n + 29 by n + 4 using long division.
To solve this, we follow the steps of long division. First, we divide the first term of the dividend, 18n^2, by the first term of the divisor, n. This gives us 18n. We then multiply this quotient by the divisor, n + 4, and subtract it from the dividend, 18n^2 + 75n + 29. This gives us a new dividend, which we repeat the process with. We continue this process until the dividend has no terms of higher degree than the divisor.
After performing the long division, we find that the quotient is 18n - 63 and the remainder is 257. Therefore, the division of the polynomial 18n^2 + 75n + 29 by n + 4 is equal to 18n - 63 with a remainder of 257.