I feel dumb asking this question. I know the roots should be positive 3 and positive 5. But when I use the equation I get a negative. I have never used the quadratic formula before so I dont understand if I am missing something basic.

You are. The quadratic formula tells you the value(s) of x such that the quadratic equals zero. In your case you’ve correctly found that x = -3 and -5 are the values of x for which x^2 + 8x + 15 = 0.

That is not what the question is asking though. It is saying if we write

what is a + b? The intention was for people to factorise.

You *can* use the quadratic formula if you want though. We know that if x = -3,

If I put x = -3 above, we get

which means that a = 3 *or* b = 3. Try the same with x = -5 and you’ll see that the other value must be 5.

The expression when factorised BTW is (x + 3)(x + 5). Notice that when x = -3 and -5, the expression is zero, as expected.

Thank you so much I did not realize the quadratic formula is for when the expression is set to equal 0. That makes complete sense.