https://file.aiquickdraw.com/mathbot/file/1727093077801s2kle59p.jpg

The problem asks to factor the expression \( 2y^2 - 2y - 4 \).

### Step-by-Step Solution:

1. **Factor out the greatest common factor (GCF):**
   The GCF of \( 2y^2 \), \( -2y \), and \( -4 \) is 2. So, we factor 2 out:
   \[
   2(y^2 - y - 2)
   \]

2. **Factor the quadratic inside the parentheses:**
   Now we need to factor \( y^2 - y - 2 \). To do this, find two numbers that multiply to \( -2 \) and add to \( -1 \). These numbers are \( -2 \) and \( 1 \).

   So, we can factor \( y^2 - y - 2 \) as:
   \[
   (y - 2)(y + 1)
   \]

3. **Write the complete factorization:**
   Now we substitute this back into the original expression:
   \[
   2(y - 2)(y + 1)
   \]

Thus, the factored form is \( 2(y - 2)(y + 1) \), which corresponds to option **B**.

---

Would you like further details or have any questions?

Here are 5 related questions to deepen understanding:

1. How do you factor quadratic expressions in general?
2. What is the importance of finding the greatest common factor (GCF)?
3. Can you always factor a quadratic using integer numbers?
4. How do you handle quadratics that cannot be factored easily?
5. What are the steps to verify if a factorization is correct?

**Tip:** Always check your factorization by expanding the factors back to the original expression!

Which expression shows the factors of 2y^2 - 2y - 4?

Learn how to factor the quadratic expression 2y^2 - 2y - 4 using the GCF and factoring techniques. This detailed guide is designed for students in Grades 8-10 and covers key algebraic concepts, such as factoring quadratics and finding the greatest common factor (GCF).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation