Question

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

Answer 1

(a+3)(a-7)<0

Answer 2

so it's the largest integer from interval (-3;7)
What is that value?

Answer 3

You have to solve the quadratic inequality (a+3)(a-7)<0
You've already had it in factored form so you take roots a=-3 and a=7
and check whether the sign of coefficient at a^2 term is positive or not(in this case it's positive (a+3)(a-7)=a^2-4a-21 so the shape of parabola is like this: Draw that like i did before and choose interval where it has negative values