High School

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Factor out the GCF from the polynomial.

[tex]x^7 + 7x^6[/tex]

[tex]x^7 + 7x^6 = \square[/tex]

(Type your answer in factored form)

Answer :

Sure! Let's factor out the Greatest Common Factor (GCF) from the given polynomial:

[tex]\[ x^7 + 7x^6 \][/tex]

### Step-by-Step Solution:

1. Identify the Greatest Common Factor (GCF):

First, look at the terms in the polynomial [tex]\( x^7 \)[/tex] and [tex]\( 7x^6 \)[/tex]. Both terms have a common factor of [tex]\( x^6 \)[/tex].

2. Factor out the GCF:

When factoring out [tex]\( x^6 \)[/tex] from each term, you divide each term by [tex]\( x^6 \)[/tex]:

- For [tex]\( x^7 \)[/tex]:
[tex]\[
x^7 \div x^6 = x^{7-6} = x
\][/tex]

- For [tex]\( 7x^6 \)[/tex]:
[tex]\[
7x^6 \div x^6 = 7
\][/tex]

So, the polynomial [tex]\( x^7 + 7x^6 \)[/tex] can be written as:
[tex]\[
x^6 (x + 7)
\][/tex]

### Final Factored Form:

Therefore, the expression [tex]\( x^7 + 7x^6 \)[/tex] factored out using the GCF is:

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

That's the factored form of the given polynomial.

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