What is the product of all constants $k$ such that the quadratic $x^2 + kx +15$ can be factored in the form $(x+a)(x+b)$, where $a$ and $b$ are integers?

Pamela has a 30-year, 5.75% mortgage on her $250,000 home. she has been paying on it for 5 years, and has recently hit some financial trouble. if her lender agreed to lower the interest rate on her $231,905.47 balance to 5.5%, what will her new payment be for the remainder of the loan?