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Let's solve this problem by factoring the given polynomial using the greatest common factor (GCF).

The polynomial given is:

\[
18x + 63
\]

First, let's find the GCF of the two terms \( 18x \) and \( 63 \).

### Step 1: Find the GCF
- The GCF of 18 and 63 is **9**, since 9 is the largest number that divides both 18 and 63 without leaving a remainder.

### Step 2: Factor the GCF out of the polynomial
Now, we can factor out **9** from both terms:

\[
18x + 63 = 9(2x + 7)
\]

### Conclusion
The correct answer is:

\[
18x + 63 = 9(2x + 7)
\]

Therefore, the correct choice is **A**, with the answer filled in as:

\[
18x + 63 = 9(2x + 7)
\]

### Summary
- The GCF is **9**.
- The factored form is **\( 9(2x + 7) \)**.

Would you like more details or have any questions about this?

### Related Questions:
1. How do you determine the greatest common factor for a polynomial?
2. Can you always factor a polynomial if the GCF is greater than 1?
3. What is the difference between factoring completely and factoring by GCF?
4. How do you check if a polynomial is prime?
5. How would you factor a polynomial with more than two terms?

### Tip:
Always start factoring by finding the greatest common factor. It makes further steps simpler if there's more factoring to do!

Factor the polynomial using the greatest common factor. If there is no common factor other than 1 and the polynomial cannot be factored, so state. 18x + 63

Learn how to factor the polynomial 18x + 63 by finding the greatest common factor (GCF). This example explains key algebraic concepts like factoring and the GCF, suitable for students in Grades 7-9.

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