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Answer :
We start with the expression
[tex]$$
-63x^7 - 7x^6.
$$[/tex]
Step 1. Identify the greatest common factor (GCF) for the coefficients.
The numerical coefficients are [tex]$-63$[/tex] and [tex]$-7$[/tex]. Since the coefficient of the highest degree term (which is [tex]$-63$[/tex]) is negative, we choose a negative common factor. The greatest common factor of [tex]$-63$[/tex] and [tex]$-7$[/tex] is [tex]$-7$[/tex].
Step 2. Identify the common variable factor.
The variable parts are [tex]$x^7$[/tex] and [tex]$x^6$[/tex]. The smallest exponent among these is [tex]$6$[/tex], so the common variable factor is [tex]$x^6$[/tex].
Step 3. Factor out the common factor [tex]$-7x^6$[/tex].
We factor [tex]$-7x^6$[/tex] from each term:
1. For the first term:
[tex]$$
-63x^7 = -7x^6 \cdot 9x \quad \text{(since } -7 \cdot 9 = -63 \text{ and } x^6 \cdot x = x^7\text{)}.
$$[/tex]
2. For the second term:
[tex]$$
-7x^6 = -7x^6 \cdot 1.
$$[/tex]
After factoring, the expression becomes
[tex]$$
-63x^7 - 7x^6 = -7x^6(9x + 1).
$$[/tex]
Thus, the answer in factored form is
[tex]$$
-7x^6(9x + 1).
$$[/tex]
[tex]$$
-63x^7 - 7x^6.
$$[/tex]
Step 1. Identify the greatest common factor (GCF) for the coefficients.
The numerical coefficients are [tex]$-63$[/tex] and [tex]$-7$[/tex]. Since the coefficient of the highest degree term (which is [tex]$-63$[/tex]) is negative, we choose a negative common factor. The greatest common factor of [tex]$-63$[/tex] and [tex]$-7$[/tex] is [tex]$-7$[/tex].
Step 2. Identify the common variable factor.
The variable parts are [tex]$x^7$[/tex] and [tex]$x^6$[/tex]. The smallest exponent among these is [tex]$6$[/tex], so the common variable factor is [tex]$x^6$[/tex].
Step 3. Factor out the common factor [tex]$-7x^6$[/tex].
We factor [tex]$-7x^6$[/tex] from each term:
1. For the first term:
[tex]$$
-63x^7 = -7x^6 \cdot 9x \quad \text{(since } -7 \cdot 9 = -63 \text{ and } x^6 \cdot x = x^7\text{)}.
$$[/tex]
2. For the second term:
[tex]$$
-7x^6 = -7x^6 \cdot 1.
$$[/tex]
After factoring, the expression becomes
[tex]$$
-63x^7 - 7x^6 = -7x^6(9x + 1).
$$[/tex]
Thus, the answer in factored form is
[tex]$$
-7x^6(9x + 1).
$$[/tex]
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Rewritten by : Barada
