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Factor the greatest common factor out of each expression.

5. [tex]\frac{5k^2}{5} - \frac{40k}{5} + \frac{10}{5}[/tex]

GCF = 5

[tex]5(k^2 - 8k + 2)[/tex]

6. [tex]50n^3 + 60n^2 - 60[/tex]

7. [tex]63m^6 - 49m^5 - 21m[/tex]

8. [tex]72x^5 - 72x^3 - 80x^2[/tex]

Answer :

Sure! Let's factor the common factor out of each expression step-by-step.

5. [tex]\(\frac{5 k^2}{5} - \frac{40 k}{5} + \frac{10}{5}\)[/tex]

First, simplify each term:

- [tex]\(\frac{5 k^2}{5}\)[/tex] simplifies to [tex]\(k^2\)[/tex].
- [tex]\(\frac{40 k}{5}\)[/tex] simplifies to [tex]\(8k\)[/tex].
- [tex]\(\frac{10}{5}\)[/tex] simplifies to [tex]\(2\)[/tex].

The expression simplifies to:

[tex]\[ k^2 - 8k + 2 \][/tex]

There is no further common factor to extract here other than 1, as the expression is already in its simplest form.

6. [tex]\(50 n^3 + 60 n^2 - 60\)[/tex]

Identify the greatest common factor (GCF) of the coefficients 50, 60, and 60, which is 10:

- Factor out 10:

[tex]\[ 10(5 n^3 + 6 n^2 - 6) \][/tex]

Here, we factored out the GCF, which is 10.

7. [tex]\(63 m^6 - 49 m^5 - 21 m\)[/tex]

Identify the common factor in the terms:

- Coefficients are 63, 49, and 21. The GCF of these coefficients is 7.
- Each term contains [tex]\(m\)[/tex], so the GCF is [tex]\(7m\)[/tex].

Factor out [tex]\(7m\)[/tex]:

[tex]\[ 7m(9 m^5 - 7 m^4 - 3) \][/tex]

We factored out the [tex]\(7m\)[/tex], which is the greatest common factor of the expression.

8. [tex]\(72 x^5 - 72 x^3 - 80 x^2\)[/tex]

Identify the greatest common factor:

- Coefficients are 72, 72, and 80. The GCF is 8.
- Each term contains at least [tex]\(x^2\)[/tex], so the GCF is [tex]\(8x^2\)[/tex].

Factor out [tex]\(8x^2\)[/tex]:

[tex]\[ 8x^2(9 x^3 - 9 x - 10) \][/tex]

Here, we factored out [tex]\(8x^2\)[/tex].

That's the step-by-step solution for factoring each expression by extracting the greatest common factor!

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