Factor out the greatest common factor from the following polynomial:

[tex]9x^7 - 72x^6 + 27x^5[/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice:

A. [tex]9x^7 - 72x^6 + 27x^5 =[/tex] [tex]\square[/tex] (Type your answer in factored form.)
B. The polynomial has no common factor other than 1.

To factor out the greatest common factor from the polynomial [tex]$9x^7 - 72x^6 + 27x^5$[/tex], we should follow these steps:

1. Identify the Greatest Common Factor (GCF) of the coefficients:
- Look at the coefficients of each term in the polynomial: 9, -72, and 27.
- The GCF of these numbers is 9.

2. Determine the common factor for the variable part:
- Notice the variable [tex]$x$[/tex] appears in all terms, with exponents 7, 6, and 5.
- The smallest exponent is 5, so the GCF for the variable part is [tex]$x^5$[/tex].

3. Combine these to get the overall GCF:
- These observations lead us to conclude that the greatest common factor of the entire polynomial is [tex]$9x^5$[/tex].

4. Factor out the GCF from each term:
- Divide each term of the polynomial by [tex]$9x^5$[/tex]:

[tex]\[
\frac{9x^7}{9x^5} = x^2
\][/tex]

[tex]\[
\frac{-72x^6}{9x^5} = -8x
\][/tex]

[tex]\[
\frac{27x^5}{9x^5} = 3
\][/tex]

5. Write the polynomial in its factored form:
- After factoring out [tex]$9x^5$[/tex], the polynomial can be written as:

[tex]\[
9x^7 - 72x^6 + 27x^5 = 9x^5(x^2 - 8x + 3)
\][/tex]

Therefore, the factored form of the polynomial is:
[tex]\[ 9x^5(x^2 - 8x + 3) \][/tex]

This is the correct factorization with the greatest common factor factored out.