https://file.aiquickdraw.com/mathbot/file/1726502153770iwt2d3ei.jpg

I see a list of quadratic equations and their factored forms. Let's go through each one to verify their correctness.

1. **Equation 1:**
   \[
   9x^2 + 9x + 2 = (3x + 2)(3x + 1)
   \]
   Let's expand the right-hand side:
   \[
   (3x + 2)(3x + 1) = 3x(3x + 1) + 2(3x + 1) = 9x^2 + 3x + 6x + 2 = 9x^2 + 9x + 2
   \]
   This matches the original equation, so it is correct.

2. **Equation 2:**
   \[
   5x^2 + 9x - 2 = (x + 2)(5x + 1)
   \]
   Expanding the right-hand side:
   \[
   (x + 2)(5x + 1) = x(5x + 1) + 2(5x + 1) = 5x^2 + x + 10x + 2 = 5x^2 + 11x + 2
   \]
   This does not match the original equation. The factored form is incorrect.

3. **Equation 3:**
   \[
   6x^2 + 23x + 15 = (x + 3)(6x + 5)
   \]
   Expanding the right-hand side:
   \[
   (x + 3)(6x + 5) = x(6x + 5) + 3(6x + 5) = 6x^2 + 5x + 18x + 15 = 6x^2 + 23x + 15
   \]
   This matches the original equation, so it is correct.

4. **Equation 4:**
   \[
   6x^2 - 13x - 15 = (3x + 5)(2x - 3)
   \]
   Let's expand the right-hand side:
   \[
   (3x + 5)(2x - 3) = 3x(2x - 3) + 5(2x - 3) = 6x^2 - 9x + 10x - 15 = 6x^2 + x - 15
   \]
   This does not match the original equation. The factored form is incorrect.

5. **Equation 5:**
   \[
   9x^2 + 3x - 2 = (3x + 2)(3x + 1)
   \]
   Expanding the right-hand side:
   \[
   (3x + 2)(3x + 1) = 3x(3x + 1) + 2(3x + 1) = 9x^2 + 3x + 6x + 2 = 9x^2 + 9x + 2
   \]
   This does not match the original equation. The factored form is incorrect.

In summary:
- Equations 1 and 3 are factored correctly.
- Equations 2, 4, and 5 are incorrectly factored.

Would you like further details or help correcting the incorrect factorizations?

Here are some related questions you might find helpful:
1. How do you factor quadratic equations in general?
2. How can you check if a factorization is correct?
3. What strategies can you use if simple factoring doesn’t work?
4. How does the discriminant help in factoring quadratics?
5. What are the different methods for solving quadratic equations?

**Tip:** Always expand your factored form to ensure it matches the original equation.

Verify and correct the factored forms of the given quadratic equations: 1. 9x^2 + 9x + 2 = (3x + 2)(3x + 1), 2. 5x^2 + 9x - 2 = (x + 2)(5x + 1), 3. 6x^2 + 23x + 15 = (x + 3)(6x + 5), 4. 6x^2 - 13x - 15 = (5x - 5), 5. 9x^2 + 3x - 2 = (3x + 2)(3x + 1).

Explore the process of factoring quadratic equations such as 9x^2 + 9x + 2 and 6x^2 + 23x + 15. Identify and correct common errors in factored forms using algebraic techniques. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation