If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often, factorising a polynomial requires some ...

You've already shown that these aren't factors. However \((x + 2)\) could be a repeated factor. In this case, though, we can rule out \((x + 2)\) as well. Why? Because the constant is \(15\).