To factor the quadratic expression \( 3x^2 + 19x + 20 \), follow these steps:

1. **Multiply the coefficient of \(x^2\)** (which is 3) by the constant term (which is 20):
   \[
   3 \times 20 = 60
   \]
   
2. Now, find two numbers that multiply to give 60 and add up to the coefficient of \(x\) (which is 19). These two numbers are 15 and 4 because:
   \[
   15 \times 4 = 60 \quad \text{and} \quad 15 + 4 = 19
   \]

3. Rewrite the middle term (19x) using these two numbers:
   \[
   3x^2 + 15x + 4x + 20
   \]

4. Factor by grouping:
   \[
   (3x^2 + 15x) + (4x + 20)
   \]
   Factor out the greatest common factor from each group:
   \[
   3x(x + 5) + 4(x + 5)
   \]

5. Now, factor out the common binomial factor \((x + 5)\):
   \[
   (3x + 4)(x + 5)
   \]

Thus, the factorization of \( 3x^2 + 19x + 20 \) is:
\[
(3x + 4)(x + 5)
\]

Would you like more details on any step or have any questions?

Here are some related questions:
1. How do you solve a quadratic equation using factoring?
2. What if the quadratic cannot be factored easily—what method should be used?
3. How do you determine the discriminant of a quadratic equation?
4. How can you verify if the factors are correct?
5. What are the applications of factoring in solving real-world problems?

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

Learn how to factor the quadratic equation 3x^2 + 19x + 20 with a detailed step-by-step solution. This guide covers key algebraic concepts, including factoring and the product and sum method. Ideal for students in Grades 9-10.

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