QuestionAugust 26, 2025

Factor each. You do not need to solve for x. 10. n^3-2744 11. l^3+1728 12. e^3-2744 13. f^3-729 14. n^3-4913 15. s^3-2744

Factor each. You do not need to solve for x. 10. n^3-2744 11. l^3+1728 12. e^3-2744 13. f^3-729 14. n^3-4913 15. s^3-2744
Factor each. You do not need to solve for x. 10. n^3-2744 11. l^3+1728 12. e^3-2744 13. f^3-729 14. n^3-4913 15. s^3-2744

Solution
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Answer

n^3 - 2744 = (n - 14)(n^2 + 14n + 196) ### l^3 + 1728 = (l + 12)(l^2 - 12l + 144) ### e^3 - 2744 = (e - 14)(e^2 + 14e + 196) ### f^3 - 729 = (f - 9)(f^2 + 9f + 81) ### n^3 - 4913 = (n - 17)(n^2 + 17n + 289) ### s^3 - 2744 = (s - 14)(s^2 + 14s + 196) Explanation 1. Recognize the Form Each expression is a difference or sum of cubes, which can be factored using the formulas: **a^3 - b^3 = (a-b)(a^2 + ab + b^2)** and **a^3 + b^3 = (a+b)(a^2 - ab + b^2)**. 2. Factor n^{3}-2744 2744 = 14^3, so n^3 - 2744 = (n - 14)(n^2 + 14n + 196). 3. Factor l^{3}+1728 1728 = 12^3, so l^3 + 1728 = (l + 12)(l^2 - 12l + 144). 4. Factor e^{3}-2744 2744 = 14^3, so e^3 - 2744 = (e - 14)(e^2 + 14e + 196). 5. Factor f^{3}-729 729 = 9^3, so f^3 - 729 = (f - 9)(f^2 + 9f + 81). 6. Factor n^{3}-4913 4913 = 17^3, so n^3 - 4913 = (n - 17)(n^2 + 17n + 289). 7. Factor s^{3}-2744 2744 = 14^3, so s^3 - 2744 = (s - 14)(s^2 + 14s + 196).

Explanation

1. Recognize the Form<br /> Each expression is a difference or sum of cubes, which can be factored using the formulas: **$a^3 - b^3 = (a-b)(a^2 + ab + b^2)$** and **$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$**.<br /><br />2. Factor $n^{3}-2744$<br /> $2744 = 14^3$, so $n^3 - 2744 = (n - 14)(n^2 + 14n + 196)$.<br /><br />3. Factor $l^{3}+1728$<br /> $1728 = 12^3$, so $l^3 + 1728 = (l + 12)(l^2 - 12l + 144)$.<br /><br />4. Factor $e^{3}-2744$<br /> $2744 = 14^3$, so $e^3 - 2744 = (e - 14)(e^2 + 14e + 196)$.<br /><br />5. Factor $f^{3}-729$<br /> $729 = 9^3$, so $f^3 - 729 = (f - 9)(f^2 + 9f + 81)$.<br /><br />6. Factor $n^{3}-4913$<br /> $4913 = 17^3$, so $n^3 - 4913 = (n - 17)(n^2 + 17n + 289)$.<br /><br />7. Factor $s^{3}-2744$<br /> $2744 = 14^3$, so $s^3 - 2744 = (s - 14)(s^2 + 14s + 196)$.
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