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The given quadratic expression \( 5x^2 - 3x - 2 \) factors completely as:

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

Would you like further explanation on how this factorization was done or any other details?

Here are some related questions you might find interesting:
1. How do you factor quadratic expressions in general?
2. What is the process for factoring by grouping?
3. How can the discriminant help determine if a quadratic can be factored?
4. What are some common mistakes when factoring quadratics?
5. How do you check if your factorization is correct?

**Tip:** To check your factorization, multiply the factors back together to see if you get the original expression.

This page explains how to factor the quadratic equation 5x^2 - 3x - 2 into its simplest terms: (x - 1)(5x + 2). Learn key algebraic concepts and the methods used for factoring quadratic expressions. Suitable for high school students in Grades 9-10.

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