Question

factor the common factor out of each expression.

1. $48x - 24c^{3} - 64c^{7}$
2. $40n^{3}+20n^{2}+32n$
3. $45k^{2}+18k+72$
4. $-6b^{6}+10b^{5}+6b^{4}$
5. $30n^{4}+6n^{3}+48n^{2}$
6. $35+50b+50b^{2}$
7. $28p^{2}+7p^{4}+42p^{7}$
8. $4r^{6}+10r^{2}+4r$
9. $-30m^{2}+15m^{3}-10m^{5}$
10. $-8x^{5}-40x^{3}-80x^{2}$

Explanation:

12) Step1: Find GCF of coefficients

GCF of 40, 20, 32 is 4.

12) Step2: Find GCF of variables

GCF of $n^3, n^2, n$ is $n$.

12) Step3: Factor out GCF

$4n(10n^2 + 5n + 8)$

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13) Step1: Find GCF of coefficients

GCF of 45, 18, 72 is 9.

13) Step2: Factor out GCF

$9(5k^2 + 2k + 8)$

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14) Step1: Find GCF of coefficients

GCF of -6, 10, 6 is 2.

14) Step2: Find GCF of variables

GCF of $b^6, b^5, b^4$ is $b^4$.

14) Step3: Factor out GCF

$2b^4(-3b^2 + 5b + 3)$

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15) Step1: Find GCF of coefficients

GCF of 30, 6, 48 is 6.

15) Step2: Find GCF of variables

GCF of $n^4, n^3, n^2$ is $n^2$.

15) Step3: Factor out GCF

$6n^2(5n^2 + n + 8)$

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16) Step1: Find GCF of coefficients

GCF of 35, 50, 50 is 5.

16) Step2: Factor out GCF

$5(7 + 10b + 10b^2)$

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17) Step1: Find GCF of coefficients

GCF of 28, 7, 42 is 7.

17) Step2: Find GCF of variables

GCF of $p^2, p^4, p^7$ is $p^2$.

17) Step3: Factor out GCF

$7p^2(4 + p^2 + 6p^5)$

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18) Step1: Find GCF of coefficients

GCF of 4, 10, 4 is 2.

18) Step2: Find GCF of variables

GCF of $r^6, r^2, r$ is $r$.

18) Step3: Factor out GCF

$2r(2r^5 + 5r + 2)$

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19) Step1: Find GCF of coefficients

GCF of -30, 15, -10 is 5.

19) Step2: Find GCF of variables

GCF of $m^2, m^3, m^5$ is $m^2$.

19) Step3: Factor out GCF

$5m^2(-6 + 3m - 2m^3)$

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20) Step1: Find GCF of coefficients

GCF of -8, -40, -80 is -8.

20) Step2: Find GCF of variables

GCF of $x^5, x^3, x^2$ is $x^2$.

20) Step3: Factor out GCF

$-8x^2(x^3 + 5x + 10)$

Answer:

1. $4n(10n^2 + 5n + 8)$
2. $9(5k^2 + 2k + 8)$
3. $2b^4(-3b^2 + 5b + 3)$
4. $6n^2(5n^2 + n + 8)$
5. $5(7 + 10b + 10b^2)$
6. $7p^2(4 + p^2 + 6p^5)$
7. $2r(2r^5 + 5r + 2)$
8. $5m^2(-6 + 3m - 2m^3)$
9. $-8x^2(x^3 + 5x + 10)$

(Note: The first problem (11) is cut off and cannot be solved with the provided image content)