6x² + 48x + 96
6(x² + 8x + 16)
6(x + 4)(x + 4) is your polynomial fully factored so I'm guessing the binomial you're looking for is (x + 4).
The equation (form) is: 
The solution of the equation is: 
Explanation:
First, let's call the number we are going to solve for "x".
Then two thirds of this number can be written as:

Then "plus 4" means add 4 we get:

"is 7" means that the above expression is equal to 7 (as follows):

The solution of the above equation is:

The answer is 2x^2-3x-2.
To solve this, you take f(x)-g(x) which is 2x^2-5-3x+3. This simplifies to 2x^2-3x-2.
1. x <= 31
2. x < 28
For number 1, x is less than or equal to 31 because the number of days in a month (represented by x) will be less than or equal to 31.
For number 2, x is less than 28 because the number of students (represented by x) in each class will always be less than 28.