To divide the polynomial by 9x^2, you can use long division or factor out 9x^2 from the numerator. I will show you both methods.
Using long division, you can set up the division as follows:
```
4x^3 - 7x^2 + 3
_________________________
9x^2 | 36x^5 - 63x^4 + 27x^3
| 36x^5 - 0x^4 + 0x^3
|---------------------
| - 63x^4 + 27x^3
| - 63x^4 + 0x^3
| ----------------
| 27x^3
| 27x^3
| -----
| 0
```
The quotient is 4x^3 - 7x^2 + 3, and the remainder is 0.
Using factoring, you can write the numerator as 9x^2(4x^3 - 7x^2 + 3), and then cancel out the common factor of 9x^2 with the denominator. The quotient is 4x^3 - 7x^2 + 3, and there is no remainder.