Is it possible to factor y=x^2 + 3x - 10 ? If so, what are the factors?

It is possible to factor it in $\mathbb{R}$, and it's factorized form is $y = \left(x - \frac{3 + \sqrt{49}}{2}\right) \left(x - \frac{3 - \sqrt{49}}{2}\right)$.
In order to know if there are real roots for this polynomial, you need to calculate $\Delta = {b}^{2} - 4 a c$. Here, $\Delta = 9 - 4 \cdot \left(- 10\right) = 49$ so it has two real roots.
They're given by the quadratic formula $\frac{- b \pm \sqrt{\Delta}}{2 a}$. We apply it to this trinomial and the roots are $\frac{- 3 \pm \sqrt{49}}{2}$