I've been doubting myself on this problem quite a bit.
The problem asks to prove that n^2 - 7n + 12 is nonnegative whenever n is an integer with n >= 3
When i went to prove this I made my basis step
p(3) = (3)^2 - 7(3) + 12 >= 0
p(3) = 9 - 21 + 21 >= 0
p(3) = 0 >= 0
after that, I assumed p(k)
p(k) = k^2 - 7k +12 >= 0
p(k) = (k-4)(k-3) > = 0
and
p(k+1) = (k+1)^2 - 7(k+1) + 12 >= 0
p(k+1) = k^2 - 5k + 6 >= 0
p(k+1) = (k-2)(k-3) >= 0
This is where I start to doubt myself.
(k-2)(k-3) >= (k-4)(k-3) >= 0
q.e.d.
(k-2)(k-3) >= 0
If I could get some feedback on this, it would be greatly appreciated.