To factor the quadratic expression \( n^2 - 7n + 12 \), follow these steps:

1. **Identify coefficients:**  
   The expression is in the form \( n^2 + bn + c \), where \( b = -7 \) and \( c = 12 \).

2. **Find two numbers that multiply to \( c \) (12) and add up to \( b \) (-7):**  
   We need two numbers that multiply to \( 12 \) and add up to \( -7 \).  
   These numbers are \( -3 \) and \( -4 \) because:
   \[
   (-3) \times (-4) = 12 \quad \text{and} \quad (-3) + (-4) = -7
   \]

3. **Write the expression in factored form:**
   \[
   n^2 - 7n + 12 = (n - 3)(n - 4)
   \]

Thus, the completely factored form of \( n^2 - 7n + 12 \) is \( (n - 3)(n - 4) \).

Would you like further details or have any questions? Here are five related questions you might find helpful:

1. How do you factor a quadratic expression when the leading coefficient is not 1?
2. Can you explain how to factor by grouping for a different quadratic expression?
3. How would the factoring process change if the quadratic expression had complex roots?
4. What is the importance of factoring in solving quadratic equations?
5. How can you verify that your factorization of a quadratic expression is correct?

**Tip:** Always double-check your factors by expanding them back to the original expression to ensure correctness.

Learn how to completely factor the quadratic expression n^2 - 7n + 12 with a step-by-step solution. This problem covers key algebraic concepts, including factoring quadratic expressions. Suitable for students in Grades 7-9.

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