Answer: (5/3) n^2 - (10/3) n + 1 - (2/n).
Explanation:
To divide (15n^4 - 30n^3 + 9n^2 - 18n) by 3n, we can simplify the expression by factoring out the greatest common factor (GCF) and then divide.
First, let's factor out the GCF from each term:
15n^4 - 30n^3 + 9n^2 - 18n
= 3n(5n^3 - 10n^2 + 3n - 6)
Now, we can divide each term by 3n:
(5n^3 - 10n^2 + 3n - 6) / 3n
To simplify the division further, we can divide each term individually:
5n^3 / 3n = (5/3) n^(3-1) = (5/3) n^2
-10n^2 / 3n = (-10/3) n^(2-1) = (-10/3) n
3n / 3n = 1
-6 / 3n = -2/n
Combining these simplified terms, we get:
(5/3) n^2 - (10/3) n + 1 - (2/n)
Therefore, (15n^4 - 30n^3 + 9n^2 - 18n) divided by 3n is equal to