Answer :
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].
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].