Use the long division method to find the result when x, cubed, plus, 9, x, squared, plus, 21, x, plus, 9x 3 +9x 2 +21x+9 is divided by x, plus, 3x+3.

I'm sorry, but your question seems to be a bit unclear. The expression you provided seems to be a bit mixed up. However, I'll try to interpret it as (x^3 + 9x^2 + 21x + 9) divided by (x + 3). Here's how you can do the long division:

1. Divide the first term in the numerator (x^3) by the first term in the denominator (x). This gives you x^2. Write this above the division line.

2. Multiply the entire denominator (x + 3) by the result from step 1 (x^2) and subtract this from the original numerator. This gives you a new numerator of 6x^2 + 21x + 9.

3. Repeat the process with the new numerator. Divide the first term (6x^2) by the first term in the denominator (x). This gives you 6x. Write this next to the x^2 above the division line.

4. Multiply the entire denominator (x + 3) by the result from step 3 (6x) and subtract this from the new numerator. This gives you a new numerator of 3x + 9.

5. Repeat the process with the new numerator. Divide the first term (3x) by the first term in the denominator (x). This gives you 3. Write this next to the 6x above the division line.

6. Multiply the entire denominator (x + 3) by the result from step 5 (3) and subtract this from the new numerator. This gives you a remainder of 0.

So, the result of the division is x^2 + 6x + 3.