Final answer:
The factor of the polynomial 8x^2 + 6xy - 9y^2 is 4x - 3y.
Step-by-step explanation:
To determine which of the given options is a factor of the polynomial 8x2 + 6xy - 9y2, we can use the factoring method. We need to check if any of the given options can be divided evenly into the polynomial, resulting in a remainder of zero.
We can start by checking option C: 4x - 3y. We divide the polynomial by 4x - 3y using long division or synthetic division. If the remainder is zero, then C is a factor.
We repeat this process for the other options to find the correct factor.
Therefore, the correct answer is option C: 4x - 3y.