A1 Rev - Factoring GCF DOTS - Free Printable

Let's solve each problem by factoring out the Greatest Common Factor (GCF) from each expression. The GCF is the largest factor that divides all terms in the expression.

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1) $ 8 + 6x^4 $

- Factors of 8: $ 2 \times 4 $
- Factors of 6: $ 2 \times 3 $
- So, GCF of coefficients: 2
- Variables: Only $ x^4 $ has a variable, but 8 has no variable → GCF of variables: 1
- So, GCF = 2

Factor out 2:

$$
8 + 6x^4 = 2(4 + 3x^4)
$$

✔ Answer: $ 2(4 + 3x^4) $

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2) $ 2n - 4 $

- Coefficients: 2 and 4 → GCF = 2
- Variable: only $ n $ appears in first term → GCF of variables = 1
- So, GCF = 2

Factor out 2:

$$
2n - 4 = 2(n - 2)
$$

✔ Answer: $ 2(n - 2) $

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3) $ 4n^9 + 12n $

- Coefficients: 4 and 12 → GCF = 4
- Variables: $ n^9 $ and $ n $ → GCF of variables = $ n $ (lowest power)
- So, GCF = $ 4n $

Factor out $ 4n $:

$$
4n^9 + 12n = 4n(n^8 + 3)
$$

✔ Answer: $ 4n(n^8 + 3) $

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4) $ 3r + 9 $

- Coefficients: 3 and 9 → GCF = 3
- Variables: only $ r $ in first term → GCF of variables = 1
- So, GCF = 3

Factor out 3:

$$
3r + 9 = 3(r + 3)
$$

✔ Answer: $ 3(r + 3) $

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5) $ -12a - 3 $

- Coefficients: -12 and -3 → GCF = 3 (ignore signs for GCF; we'll keep negative sign inside or outside)
- But note: both are negative → we can factor out -3 to make it simpler

Factor out -3:

$$
-12a - 3 = -3(4a + 1)
$$

✔ Answer: $ -3(4a + 1) $

*(Alternatively, you could factor out 3: $ 3(-4a - 1) $, but factoring out negative makes the inside positive — preferred style.)*

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6) $ 5r + 4r^4 $

- Coefficients: 5 and 4 → GCF = 1
- Variables: $ r $ and $ r^4 $ → GCF = $ r $
- So, GCF = r

Factor out $ r $:

$$
5r + 4r^4 = r(5 + 4r^3)
$$

✔ Answer: $ r(5 + 4r^3) $

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7) $ 12n^5 + 16n^3 $

- Coefficients: 12 and 16 → GCF = 4
- Variables: $ n^5 $ and $ n^3 $ → GCF = $ n^3 $
- So, GCF = $ 4n^3 $

Factor out $ 4n^3 $:

$$
12n^5 + 16n^3 = 4n^3(3n^2 + 4)
$$

✔ Answer: $ 4n^3(3n^2 + 4) $

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8) $ -9x^3 - 12x $

- Coefficients: -9 and -12 → GCF = 3 (but both negative → factor out -3)
- Variables: $ x^3 $ and $ x $ → GCF = $ x $
- So, GCF = $ -3x $

Factor out $ -3x $:

$$
-9x^3 - 12x = -3x(3x^2 + 4)
$$

✔ Answer: $ -3x(3x^2 + 4) $

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✔ Final Answers:

1) $ 2(4 + 3x^4) $
2) $ 2(n - 2) $
3) $ 4n(n^8 + 3) $
4) $ 3(r + 3) $
5) $ -3(4a + 1) $
6) $ r(5 + 4r^3) $
7) $ 4n^3(3n^2 + 4) $
8) $ -3x(3x^2 + 4) $

Let me know if you'd like explanations with diagrams or steps broken down further!