1. **Problem Statement:** We want to understand how to factor trinomials of the form $x^2 + bx + c$. 2. **Formula and Rules:** A trinomial $x^2 + bx + c$ can be factored into two binomials $(x + m)(x + n)$ where $m$ and $n$ are numbers such that: - $m + n = b$ (the coefficient of $x$) - $m \times n = c$ (the constant term) 3. **Step-by-step Example 1:** Factor $x^2 + 5x + 6$ - Find two numbers that add to 5 and multiply to 6. - These numbers are 2 and 3 because $2 + 3 = 5$ and $2 \times 3 = 6$. - So, $x^2 + 5x + 6 = (x + 2)(x + 3)$. 4. **Step-by-step Example 2:** Factor $x^2 - 3x - 10$ - Find two numbers that add to -3 and multiply to -10. - These numbers are -5 and 2 because $-5 + 2 = -3$ and $-5 \times 2 = -10$. - So, $x^2 - 3x - 10 = (x - 5)(x + 2)$. 5. **Explanation:** The key is to find two numbers that satisfy both the sum and product conditions. This method works well when the leading coefficient is 1. 6. **Summary:** To factor $x^2 + bx + c$, find $m$ and $n$ such that $m + n = b$ and $mn = c$, then write the factorization as $(x + m)(x + n)$.