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To factor the quadratic expression:

\[
5y^2 + 9y - 14
\]

we need to find two numbers that multiply to \(5 \cdot (-14) = -70\) and add up to 9. Let's proceed step-by-step:

1. **Find factors**: We need numbers that multiply to -70 and add to 9. These numbers are 14 and -5.
   
2. **Rewrite the middle term**: Use the numbers found to rewrite the expression:
   
   \[
   5y^2 + 14y - 5y - 14
   \]

3. **Factor by grouping**: Group the terms:
   
   \[
   (5y^2 + 14y) - (5y + 14)
   \]

4. **Factor each group**:
   
   \[
   5y(y + 2) - 7(y + 2)
   \]

5. **Factor out the common factor**:

   \[
   (5y - 7)(y + 2)
   \]

Thus, the factored form is:

\[
(5y - 7)(y + 2)
\]

Would you like more details or have any specific questions?

### Related Questions:
1. What is the method for factoring a quadratic expression with a leading coefficient other than 1?
2. How do you verify that the factorization of a quadratic expression is correct?
3. What are the possible techniques for factoring different types of polynomials?
4. Can all quadratic expressions be factored using integers?
5. What is the role of the discriminant in determining factorability?

**Tip:** Always check your factorization by expanding it back to ensure you obtain the original expression.

Factor the quadratic expression: 5y^2 + 9y - 14

Learn how to factor the quadratic expression 5y^2 + 9y - 14 step by step using the product-sum method. This solution demonstrates key algebraic concepts suitable for students in Grades 9-10.

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