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64c^3+1 factor each polynomial completely. make sure to chek for a gcf first
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GPT-5 mini
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First check GCF: 64c^3 + 1 has no common factor other than 1.
Recognize it as a sum of cubes: (4c)^3 + 1^3. Use a^3 + b^3 = (a + b)(a^2 - ab + b^2):
64c^3 + 1 = (4c + 1)(16c^2 - 4c + 1).
The quadratic 16c^2 - 4c + 1 has discriminant (-4)^2 - 4(16)(1) = 16 - 64 = -48, so it does not factor further over the rationals.
Recognize it as a sum of cubes: (4c)^3 + 1^3. Use a^3 + b^3 = (a + b)(a^2 - ab + b^2):
64c^3 + 1 = (4c + 1)(16c^2 - 4c + 1).
The quadratic 16c^2 - 4c + 1 has discriminant (-4)^2 - 4(16)(1) = 16 - 64 = -48, so it does not factor further over the rationals.
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