To factor the quadratic expression \( 5x^2 + 24x + 16 \), we use the method of splitting the middle term or factoring by grouping.

### Step-by-step process:

1. **Multiply the coefficient of \( x^2 \) (which is 5) and the constant term (which is 16):**

   \[
   5 \times 16 = 80
   \]

2. **Find two numbers that multiply to 80 and add to the coefficient of \( x \) (which is 24):**

   The numbers are 20 and 4 because:

   \[
   20 \times 4 = 80 \quad \text{and} \quad 20 + 4 = 24
   \]

3. **Rewrite the middle term \( 24x \) as \( 20x + 4x \):**

   \[
   5x^2 + 20x + 4x + 16
   \]

4. **Group the terms:**

   \[
   (5x^2 + 20x) + (4x + 16)
   \]

5. **Factor out the greatest common factor (GCF) from each group:**

   \[
   5x(x + 4) + 4(x + 4)
   \]

6. **Factor out the common binomial factor \( (x + 4) \):**

   \[
   (5x + 4)(x + 4)
   \]

So, the factorization of \( 5x^2 + 24x + 16 \) is:

\[
(5x + 4)(x + 4)
\]

Would you like more details or have any questions?

### Related questions:
1. How do you factor a quadratic equation with a negative middle term?
2. Can every quadratic expression be factored into two binomials?
3. What is the difference between factoring and solving a quadratic equation?
4. How do you apply the quadratic formula to this equation?
5. How can you verify if the factorization is correct?

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

Learn how to factor the quadratic equation 5x^2 + 24x + 16 with a detailed step-by-step solution. This tutorial covers the method of factoring by grouping, a key algebraic concept for students in Grades 9-10.

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