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?

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.