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The question asks you to factor the expression \(2x^2 - 14xy + 3x - 21y\), using the method of grouping and factoring out common factors.

### Let's solve this step by step:

1. **Step 1: Group the terms.**
   \[
   (2x^2 - 14xy) + (3x - 21y)
   \]
   We group the first two terms together and the last two terms together.

2. **Step 2: Factor out the greatest common factor (GCF) from each group.**
   - From \(2x^2 - 14xy\), the GCF is \(2x\), so:
     \[
     2x(x - 7y)
     \]
   - From \(3x - 21y\), the GCF is \(3\), so:
     \[
     3(x - 7y)
     \]

3. **Step 3: Factor out the common binomial.**
   Now, we see that both groups have a common factor of \((x - 7y)\):
   \[
   (2x + 3)(x - 7y)
   \]

### Answer:
The final factored form of the expression is \((2x + 3)(x - 7y)\).

### To match the multiple-choice options:
The question asks, "What needs to be done with the last two terms?"
- From the last two terms \((3x - 21y)\), we removed a common factor of **3**.

Therefore, the correct answer is **B**: "Remove a common factor of 3 from the last two terms."

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Do you want more details or have any questions? Here are five related questions to consider:

1. What is the general method for factoring by grouping?
2. How do you identify the greatest common factor (GCF) in an expression?
3. How can you check if your factorization is correct by expanding the factored form?
4. Are there cases where factoring by grouping does not work?
5. Can the grouping method be applied to higher-degree polynomials?

**Tip:** Always check your factorization by distributing the terms to ensure they match the original expression!

To factor 2x^2 - 14xy + 3x - 21y, a common factor of 2x must first be removed from the first two terms. What needs to be done with the last two terms? What should the final answer be?

Learn how to factor the quadratic expression 2x^2 - 14xy + 3x - 21y using the factoring by grouping method. This solution demonstrates key algebraic techniques, including identifying the greatest common factor (GCF) and grouping terms, suitable for Grades 8-10 students.

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