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The problem shown in the image is asking to factor the quadratic polynomial \( 4x^2 + 20x + 16 \).

Let's solve this step by step:

1. **Identify the coefficients**:
   - \( a = 4 \) (coefficient of \( x^2 \))
   - \( b = 20 \) (coefficient of \( x \))
   - \( c = 16 \) (constant term)

2. **Check for common factors**: First, notice that 4 is a common factor in all terms:
   \[
   4x^2 + 20x + 16 = 4(x^2 + 5x + 4)
   \]

3. **Factor the quadratic expression inside the parentheses**:
   \[
   x^2 + 5x + 4
   \]
   We need to find two numbers that multiply to \( 4 \) (the constant term) and add up to \( 5 \) (the coefficient of \( x \)). These numbers are 4 and 1.

   Thus, we can factor \( x^2 + 5x + 4 \) as:
   \[
   (x + 4)(x + 1)
   \]

4. **Combine the factor of 4**: 
   \[
   4(x + 4)(x + 1)
   \]

Thus, the factored form of the polynomial is:
\[
4(x + 4)(x + 1)
\]

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions:
1. How do you factor a quadratic when the leading coefficient isn't 1?
2. What methods can be used to factor polynomials?
3. How can you verify if your factorization is correct?
4. What is the greatest common factor (GCF), and how is it used in factoring?
5. How do you factor quadratics that cannot be factored easily?

**Tip**: Always check if there is a greatest common factor (GCF) in a polynomial before factoring. This simplifies the process!

Factor the given polynomial: 4x^2 + 20x + 16

Learn how to factor the quadratic polynomial 4x^2 + 20x + 16. This detailed step-by-step guide demonstrates factoring by finding the greatest common factor and splitting the middle term. Ideal for students in Grades 9-10.

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