1️⃣ Factoring helps us find where a graph crosses the $x$-axis. 🌈 2️⃣ Imagine the equation $y = x^2 - 5x + 6$. We want to find where $y=0$. 3️⃣ Factoring $x^2 - 5x + 6$ means finding numbers that multiply to $6$ and add to $-5$. 4️⃣ Those numbers are $-2$ and $-3$, so we write: $$x^2 - 5x + 6 = (x - 2)(x - 3)$$ 5️⃣ To find the intercepts, set each factor to zero: $$x - 2 = 0 \Rightarrow x=2$$ $$x - 3 = 0 \Rightarrow x=3$$ 6️⃣ So, the graph crosses the $x$-axis at $x=2$ and $x=3$. 🎯 Great! Factoring helps us find these important points called "intercepts." 🌟