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The given expression to factor is \( 4x^2 - 3x - 10 \).

### Steps to factor the quadratic:

We need to find two numbers that multiply to \( 4 \times (-10) = -40 \) and add up to \( -3 \).

- Factors of \(-40\) that add to \(-3\) are \(-8\) and \(5\), since \(-8 + 5 = -3\).

Now, split the middle term using these numbers:
\[
4x^2 - 8x + 5x - 10
\]

Next, group the terms:
\[
(4x^2 - 8x) + (5x - 10)
\]

Factor out the greatest common factors (GCF) from each group:
\[
4x(x - 2) + 5(x - 2)
\]

Now, factor out the common binomial factor \( (x - 2) \):
\[
(4x + 5)(x - 2)
\]

Thus, the factored form of the expression is:
\[
(4x + 5)(x - 2)
\]

Would you like further explanation on any of these steps?

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Here are 5 related questions you might find useful:

1. How do you factor a quadratic expression when the leading coefficient is greater than 1?
2. What is the "AC method" in factoring trinomials?
3. How can you verify if your factorization of a quadratic is correct?
4. What should you do if a quadratic is not factorable with real numbers?
5. How does factoring a quadratic relate to solving quadratic equations?

**Tip:** Always double-check your factorization by expanding the factors to ensure they give you the original expression.

Learn how to factor the quadratic expression 4x^2 - 3x - 10 with a step-by-step solution. This problem covers key algebra concepts such as factoring, using the AC method, and applying the distributive property. Suitable for students in Grades 8-10.

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