Different rate 6x^3 _5x^2 +1 /3x^2?

To divide the polynomial 6x^3 - 5x^2 + 1 by 3x^2, we can perform long division:

First, divide the leading term of the dividend by the leading term of the divisor:
6x^3 / 3x^2 = 2x

Next, multiply the entire divisor by the result obtained in the previous step:
2x * 3x^2 = 6x^3

Subtract this result from the original dividend:
6x^3 - 6x^3 = 0

Bring down the next term:
-5x^2

Now, repeat the process:
-5x^2 / 3x^2 = -5/3

Multiply the entire divisor by the result obtained:
-5/3 * 3x^2 = -5x^2

Subtract this result from the remaining terms:
-5x^2 - (-5x^2) = 0

Bring down the last term:
1

Since there are no more terms to bring down, the final result is:
2x - 5/3