Final answer:
To solve (6x² -25x -25)/(6x + 5), we can use polynomial long division. The quotient is x - 25/6 and the remainder is 0.
Step-by-step explanation:
When dividing (6x² - 25x - 25) by (6x + 5), we can use polynomial long division to find the quotient and remainder. The first step is to divide 6x by 6x, which gives us x. Then we multiply (6x + 5) by x and subtract the result from (6x² - 25x - 25). This gives us 6x² - x(6x + 5) - 25. We then divide -25 by 6x, which gives us -25/6x. We bring down the -25 and repeat the process until we have no more terms to bring down. In the end, we have a quotient of x - 25/6 and a remainder of 0.