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The given quadratic expression is:

\[
5x^2 + 9x - 2
\]

We are asked to factor it in the form:

\[
(x + ?)(?x - ?)
\]

### Step-by-Step Solution:

1. **Multiply the coefficient of \( x^2 \) (which is 5) with the constant term (which is -2):**
   \[
   5 \times -2 = -10
   \]

2. **Now, we need two numbers that multiply to give -10 and add to give the middle coefficient, which is +9.**  
   The numbers are **10** and **-1**, because:
   \[
   10 \times -1 = -10 \quad \text{and} \quad 10 + (-1) = 9
   \]

3. **Rewrite the middle term \( 9x \) using these two numbers:**
   \[
   5x^2 + 10x - x - 2
   \]

4. **Now, group the terms:**
   \[
   (5x^2 + 10x) - (x + 2)
   \]

5. **Factor each group:**
   \[
   5x(x + 2) - 1(x + 2)
   \]

6. **Factor out the common binomial \( (x + 2) \):**
   \[
   (5x - 1)(x + 2)
   \]

Thus, the factorization of \( 5x^2 + 9x - 2 \) is:

\[
(5x - 1)(x + 2)
\]

Let me know if you'd like further explanation or have any questions!

Here are 5 related questions:
1. How do you factor a quadratic equation when the leading coefficient is greater than 1?
2. What is the relationship between factoring and the quadratic formula?
3. Can all quadratic equations be factored? Why or why not?
4. How can the distributive property help verify factorizations?
5. What are other methods to solve quadratic equations apart from factoring?

**Tip:** When factoring quadratics, always check your factorization by expanding it to ensure you get back the original equation.

Factor the quadratic expression 5x^2 + 9x - 2.

Learn how to factor the quadratic expression 5x^2 + 9x - 2 using the product-sum method. Follow the step-by-step solution to break down the quadratic and factor it into two binomials. This algebra problem is perfect for students in Grades 8-10.

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