Write in factored form by factoring out the greatest common factor (or a negative common factor if the coefficient of the term of greatest degree is negative).

[tex]-77x^7 - 7x^6[/tex]

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

A. [tex]-77x^7 - 7x^6 = \square[/tex]

B. There is no common factor except 1.

Sure! Let's solve the problem step-by-step by factoring out the greatest common factor:

We are given the expression:
[tex]\(-77x^7 - 7x^6\)[/tex]

Step 1: Identify the common factor.
- Look at the coefficients: The coefficients are -77 and -7. The greatest common factor of these numbers is 7.
- Look at the variables: The expression includes [tex]\(x^7\)[/tex] and [tex]\(x^6\)[/tex]. The smallest power of [tex]\(x\)[/tex] that appears in both terms is [tex]\(x^6\)[/tex].

Overall, the greatest common factor of the entire expression is [tex]\(7x^6\)[/tex]. Since the leading term has a negative coefficient, we should factor out [tex]\(-7x^6\)[/tex].

Step 2: Factor out [tex]\(-7x^6\)[/tex] from each term.
- From [tex]\(-77x^7\)[/tex]: When you divide [tex]\(-77x^7\)[/tex] by [tex]\(-7x^6\)[/tex], you get [tex]\(11x\)[/tex].
- From [tex]\(-7x^6\)[/tex]: When you divide [tex]\(-7x^6\)[/tex] by [tex]\(-7x^6\)[/tex], you get [tex]\(1\)[/tex].

Step 3: Write the factored expression.
After factoring out [tex]\(-7x^6\)[/tex], the expression becomes:
[tex]\(-7x^6(11x + 1)\)[/tex]

So, the expression in factored form is:
[tex]\(-7x^6(11x + 1)\)[/tex]

This matches with choice A. Therefore, the correct factored form is [tex]\(-7x^6(11x + 1)\)[/tex].