The expression $x^2 + 13x + 30$ can be written as $(x + a)(x + b),$ and the expression $x^2 + 5x - 50$ written as $(x + b)(x - c)$, where $a$, $b$, and $c$ are integers. What is the value of $a + b + c$?

Try to factor by grouping.

\(x^2 + 13x + 30 = (x^2 + 10x) + (3x + 30) = x(x + 10) + 3(x + 10) = (x + 3)(x + 10)\)

\(x^2 + 5x - 50 = x^2 + 10x - (5x + 50) = x(x + 10) - 5(x + 10) = (x - 5)(x + 10)\)

The rest is trivial.

Hints: Find b first.