Answer:
In order to obtain the correct answer we have to analyze the terms of the polynomial. Notice that the first term has 64 as coefficient, and 64=8*8 and the third term is 9, and 9=3*3. Those facts suggest that the factorization can be done in term of a square binomial. This assumption is confirmed noticing that 48=2*8*3. Therefore, 64x^2+48x+9 = (8x+3)(8x+3).
The answer can be checked expanding the product (8x+3)(8x+3).
Explanation: