Question

What is the largest integer for which (a+3)(a-7) us negative?

Answer 1

6

Answer 2

(a-7) will be negative for any integer less than or equal to 6
Also, (a+3) will be positive (or 0) for any integer greater than -2
So, using the max of 6 gives 9*-1=-9, so 6 is the max

Answer 3

Anything more than 6 will result in a positive number (or 0 if a=7)