https://file.aiquickdraw.com/mathbot/file/17286234568795ie0tjvk.jpg

This quiz is about factoring trinomials. The problem given is:

\[
x^2 + 19x + 18
\]

### Let's walk through the steps provided in the image:

1. **Write two sets of parentheses**:
   You need to factor the trinomial into two binomials. The first term is \(x^2\), so you can write:

   \[
   (x \ \ \ )(x \ \ \ )
   \]

2. **Find two numbers that multiply to 18 and add up to 19**:
   The constant term is 18, and the coefficient of the middle term is 19. We need to find two numbers that multiply to 18 and add to 19. These numbers are 1 and 18, since:

   \[
   1 \times 18 = 18 \quad \text{and} \quad 1 + 18 = 19
   \]

3. **Fill in the parentheses**:
   Using the two numbers found (1 and 18), the factorization becomes:

   \[
   (x + 1)(x + 18)
   \]

4. **Check your answer by multiplying**:
   You can expand \( (x + 1)(x + 18) \) to verify:

   \[
   (x + 1)(x + 18) = x^2 + 18x + 1x + 18 = x^2 + 19x + 18
   \]

This matches the original trinomial, so the factorization is correct.

---

Would you like more details or have any questions?

### Related questions to expand your understanding:
1. How would you factor a trinomial where the leading coefficient is not 1?
2. Can you factor a trinomial like \(x^2 - 19x + 18\)?
3. What is the difference between factoring and expanding expressions?
4. How would you handle a case where no integers multiply to the constant term and add to the middle term?
5. How can you use the quadratic formula to solve a factored trinomial?

**Tip**: Always check your factorization by expanding back to verify the original expression.

Learn how to factor the quadratic trinomial x^2 + 19x + 18 using simple algebraic techniques. This problem covers key concepts like finding factors of constants and checking your work through expansion. Ideal for Grades 8-10.

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