+47 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 $a + b + c$?
+526 x2+13x+30=x2+3x+10x+30
=x(x+3)+10(x+3)
=(x+3)(x+10)
⇒ a = 3 and b = 10
x2+5x−50=x2+10x−5x−50
=x(x+10)−5(x+10)
=(x+10)(x−5)
⇒ c = 5
a+b+c=3+10+5=18
+876 @amygdaleon305, nice solution! Next time, consider using the \begin{align*} environment.
Your solution in that environment(you can view the code by double-clicking the TeX and clicking view TeX commands):
x2+13x+30=x2+3x+10x+30=x(x+3)+10(x+3)=(x+3)(x+10)
$\Rightarrow$ $a = 3$ and $b = 10$
x2+5x−50=x2+10x−5x−50=x(x+10)−5(x+10)=(x+10)(x−5)
$\Rightarrow c = 5$
$a + b + c = 3 + 10 + 5 = \boxed{18}$
+876 $x^2 + 13x + 30 = (x+10)(x+3)$
$x^2 + 5x - 50 = (x+10)(x-5)$
$10 + 3 + 5 = \boxed{18}$
