To factor the quadratic expression \(3m^2 - 11m - 4\), follow these steps:

1. **Multiply the coefficient of \(m^2\) (which is 3) by the constant term (which is -4)**. This gives us:
   \[
   3 \times (-4) = -12
   \]

2. **Find two numbers that multiply to give -12 and add up to the middle coefficient (-11)**. The numbers are -12 and 1 because:
   \[
   -12 \times 1 = -12 \quad \text{and} \quad -12 + 1 = -11
   \]

3. **Rewrite the middle term (-11m) using -12 and 1**:
   \[
   3m^2 - 12m + m - 4
   \]

4. **Group the terms**:
   \[
   (3m^2 - 12m) + (m - 4)
   \]

5. **Factor each group**:
   \[
   3m(m - 4) + 1(m - 4)
   \]

6. **Factor out the common binomial factor**:
   \[
   (m - 4)(3m + 1)
   \]

So, the factored form of \(3m^2 - 11m - 4\) is:
\[
(m - 4)(3m + 1)
\]

Would you like any further explanation on any of these steps?

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Here are 5 related questions to deepen your understanding:
1. How do you factor quadratics where the coefficient of \(m^2\) is 1?
2. Can you factor the expression \(2x^2 - 5x + 3\)?
3. What is the method for solving quadratic equations using factoring?
4. How do you check if a factorization is correct?
5. How would you factor a quadratic expression with positive terms only?

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

Learn how to factor the quadratic expression 3m^2 - 11m - 4 using factoring by grouping. This problem demonstrates key algebraic techniques, including finding factors of a trinomial and applying the zero product property. Suitable for students in Grades 8-10.

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