https://r2.erweima.ai/mathbot/image/1726095444651thgsep8o.jpg

Let's work through the factorization of each quadratic expression from the image:

1. **\(x^2 + 8x + 7\)**
   - We need two numbers that multiply to \(7\) and add up to \(8\). These numbers are \(7\) and \(1\).
   - Factorization: \((x + 7)(x + 1)\)

2. **\(x^2 - 9x + 14\)**
   - We need two numbers that multiply to \(14\) and add up to \(-9\). These numbers are \(-7\) and \(-2\).
   - Factorization: \((x - 7)(x - 2)\)

3. **\(x^2 - 8x - 9\)**
   - We need two numbers that multiply to \(-9\) and add up to \(-8\). These numbers are \(-9\) and \(1\).
   - Factorization: \((x - 9)(x + 1)\)

4. **\(x^2 + 12x - 13\)**
   - We need two numbers that multiply to \(-13\) and add up to \(12\). These numbers are \(13\) and \(-1\).
   - Factorization: \((x + 13)(x - 1)\)

Would you like further details or explanations on any of these steps?

Here are five follow-up questions you might find useful:

1. How do we determine which numbers to use in factorization?
2. What happens if a quadratic expression cannot be factored over the integers?
3. How would you factor a quadratic expression where the coefficient of \(x^2\) is not 1?
4. What are some special cases in quadratic factorization (like perfect square trinomials)?
5. How can we verify that our factorization is correct?

**Tip**: Always check your factorization by expanding the factors back out to make sure you return to the original expression.

Factorize the following expressions: 1) x^2 + 8x + 7, 2) x^2 - 9x + 14, 3) x^2 - 8x - 9, 4) x^2 + 12x - 13

Learn how to factor quadratic expressions such as x^2 + 8x + 7 and x^2 - 8x - 9. This detailed guide explains the step-by-step process, including using factors of c to get the sum of b. Ideal for Grades 9-10 students.

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