factor the expression completely: -63x^5 + 72

To factor the expression \(-63x^5 + 72\) completely, follow these steps:

1. **Identify the Greatest Common Factor (GCF)**:

   The GCF of the coefficients \(-63\) and \(72\) is \(9\). Both terms do not share a variable factor because \(72\) does not have \(x\). So, the GCF of the entire expression is \(9\).

2. **Factor out the GCF**:

   Factor out \(9\) from each term:

   \[
   -63x^5 + 72 = 9(-7x^5 + 8)
   \]

3. **Check for further factorization**:

   Now, look at the expression inside the parentheses: \(-7x^5 + 8\). It contains two terms:
   
   - The term \(-7x^5\) is a product of \(-7\) and \(x^5\).
   - The term \(8\) is a constant.

   Since \(-7\) and \(8\) do not have any common factors, and the expression \(-7x^5 + 8\) cannot be factored further using integer coefficients, it is considered fully factored.

The completely factored form of the expression is:

\[
9(-7x^5 + 8)
\]

Would you like more details or have any questions about this factorization process? Here are some related questions you might explore:

1. How do you find the greatest common factor of a set of numbers?
2. What are some methods to check if a polynomial can be factored further?
3. How do you factor a polynomial that includes more than two terms?
4. What are the steps for factoring polynomials with higher powers of \(x\)?
5. Can you factor the expression if given a different set of coefficients?

**Tip:** Always start by factoring out the greatest common factor when working with polynomial expressions; this simplifies the process and reduces the risk of missing any factors.

Factor the expression completely: -63x^5 + 72

Learn how to factor the polynomial expression -63x^5 + 72 completely using the Greatest Common Factor (GCF). This solution includes step-by-step instructions for finding the GCF and factoring polynomials. Suitable for students in Grades 8-10.

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