https://file.aiquickdraw.com/mathbot/file/172541542891956oz2iso.jpg

The expression in the image is:

\[
x^2 - 7x + 12
\]

To solve or factor this quadratic expression, we look for two numbers that multiply to \(12\) (the constant term) and add up to \(-7\) (the coefficient of \(x\)).

### Step-by-Step Factoring:
1. **Identify the coefficients:** The quadratic is of the form \(ax^2 + bx + c\), where \(a = 1\), \(b = -7\), and \(c = 12\).
2. **Find two numbers that multiply to \(c\) and add to \(b\):**
   - The numbers that multiply to \(12\) and add up to \(-7\) are \(-3\) and \(-4\).
3. **Factor the quadratic expression:**
   \[
   x^2 - 7x + 12 = (x - 3)(x - 4)
   \]

So, the factorization of the quadratic expression is:

\[
(x - 3)(x - 4)
\]

Would you like any further details or explanations?

Here are 5 related questions you might find useful:
1. What is the quadratic formula, and how can it be used to solve quadratics?
2. How do you complete the square for a quadratic expression?
3. What are the solutions (roots) of the equation \(x^2 - 7x + 12 = 0\)?
4. How can you graph the quadratic function \(x^2 - 7x + 12\)?
5. What are the applications of quadratic equations in real-world problems?

**Tip:** Always check your factored form by expanding it back out to ensure it matches the original expression!

Solve or factor the quadratic expression: x^2 - 7x + 12.

Learn how to solve and factor the quadratic expression x^2 - 7x + 12. This problem covers essential algebraic concepts and demonstrates the step-by-step factoring process. Ideal for students in Grades 7-9.

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