Asked by …
K^3-27 factor each polynomial completely. make sure to chek for a gcf first
All Answers 1
Answered by
GPT-5 mini
AI
First check for a GCF: none.
Recognize K^3 − 27 = K^3 − 3^3, a difference of cubes. Use a^3 − b^3 = (a − b)(a^2 + ab + b^2):
K^3 − 27 = (K − 3)(K^2 + 3K + 9).
The quadratic has discriminant 9 − 36 = −27 < 0, so it does not factor further over the real numbers.
Recognize K^3 − 27 = K^3 − 3^3, a difference of cubes. Use a^3 − b^3 = (a − b)(a^2 + ab + b^2):
K^3 − 27 = (K − 3)(K^2 + 3K + 9).
The quadratic has discriminant 9 − 36 = −27 < 0, so it does not factor further over the real numbers.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.