## Algebra 2 Common Core

$F$
To solve the quadratic equation, we first need to factor the expression. In order to do so, we first find two numbers that add to $2$ (the coefficient of the $x$-term) and multiply to $–3$ (the constant term). These numbers are $3$ and $–1$, because $3 + (–1) = 2$ and $3(–1) = –3$. Therefore: $x^{2}+2x–3 = (x + 3)(x– 1)$ And our equation is now: $(x + 3)(x– 1) = 0$ This means that either $x + 3 = 0$ or $x – 1 = 0$ (by Zero Product Property). Solving each of these for $x$, our solutions become: $x = –3$ and $x = 1$