Factor out the greatest common factor from the following polynomial:

[tex]8x^5 - 48x^4 + 16x^3[/tex]

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

A. [tex]8x^5 - 48x^4 + 16x^3 = \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 (GCF) from the polynomial [tex]$8x^5 - 48x^4 + 16x^3$[/tex], follow these steps:

1. Identify the GCF of the coefficients:
- The coefficients of the terms are 8, 48, and 16.
- The GCF of these numbers is 8.

2. Identify the smallest power of [tex]$x$[/tex] present in each term:
- The terms have powers of [tex]$x$[/tex] that are 5, 4, and 3.
- The smallest power of [tex]$x$[/tex] is [tex]$x^3$[/tex].

3. Combine the GCF of the coefficients and the smallest power of [tex]$x$[/tex]:
- The GCF of the entire polynomial is [tex]$8x^3$[/tex].

4. Factor out [tex]$8x^3$[/tex] from each term:
- For the first term: [tex]$8x^5$[/tex], divide by [tex]$8x^3$[/tex] to get [tex]$x^2$[/tex].
- For the second term: [tex]$-48x^4$[/tex], divide by [tex]$8x^3$[/tex] to get [tex]$-6x$[/tex].
- For the third term: [tex]$16x^3$[/tex], divide by [tex]$8x^3$[/tex] to get 2.

5. Write the polynomial in factored form:
[tex]\[
8x^5 - 48x^4 + 16x^3 = 8x^3(x^2 - 6x + 2)
\][/tex]

Therefore, the polynomial [tex]$8x^5 - 48x^4 + 16x^3$[/tex] factors to [tex]$8x^3(x^2 - 6x + 2)$[/tex].

Select choice A:
- [tex]$8x^5 - 48x^4 + 16x^3 = 8x^3(x^2 - 6x + 2)$[/tex]