Factor out the greatest common factor. Simplify the factors, if possible.

[tex]14x^6 - 42x^7 + 7x^8[/tex]

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

A. [tex]14x^6 - 42x^7 + 7x^8 = \square[/tex]
(Type your answer in factored form. Simplify your answer.)

B. There is no common factor other than 1.

To factor out the greatest common factor from the expression [tex]\(14x^6 - 42x^7 + 7x^8\)[/tex], we need to follow these steps:

1. Identify the numerical greatest common factor (GCF):
- The coefficients of the terms are 14, 42, and 7.
- The greatest common factor of 14, 42, and 7 is 7.

2. Identify the variable part of the GCF:
- The variable [tex]\(x\)[/tex] is present in all terms with exponents 6, 7, and 8.
- The smallest exponent among these is 6, so [tex]\(x^6\)[/tex] is the greatest common factor for the variable part.

3. Factor out the GCF from each term:
- [tex]\(14x^6\)[/tex] becomes [tex]\(7x^6 \times 2\)[/tex].
- [tex]\(-42x^7\)[/tex] becomes [tex]\(7x^6 \times (-6x)\)[/tex].
- [tex]\(7x^8\)[/tex] becomes [tex]\(7x^6 \times x^2\)[/tex].

4. Write the expression in factored form:
- Combine these factored terms to express the original expression as a product of the GCF and another polynomial.

The factored form of the expression [tex]\(14x^6 - 42x^7 + 7x^8\)[/tex] is:

[tex]\[
7x^6(x^2 - 6x + 2)
\][/tex]

This is the simplified, factored form of the original expression using the greatest common factor.