Discussion Overview
The discussion revolves around factoring the polynomial $$x^{3}-27$$, specifically seeking to express it in the form $$(x - A)(x^{2} + Bx + C)$$ and determining the values of A, B, and C. The context is primarily homework-related, focusing on the application of the difference of cubes formula.
Discussion Character
- Homework-related, Mathematical reasoning
Main Points Raised
- One participant expresses uncertainty about factoring the polynomial and seeks help with identifying A, B, and C.
- Another participant suggests using the difference of cubes formula, indicating that $$x^{3}-27$$ can be rewritten as $$x^3-3^3$$.
- A subsequent reply reiterates the hint about the difference of cubes formula and provides a partial factorization as $$(x - 3)(x^{2} + 3x + C)$$.
- Another participant prompts for clarification on the value of C based on the difference of cubes formula.
- A participant claims to have found C to be 9, indicating a potential resolution for that variable.
- Another participant acknowledges the previous response positively, suggesting agreement on the finding.
Areas of Agreement / Disagreement
There appears to be a general agreement on the approach to factor the polynomial using the difference of cubes formula, and one participant claims to have determined the value of C. However, the discussion does not fully resolve the values of A and B, leaving some uncertainty.
Contextual Notes
The discussion does not clarify the assumptions made regarding the values of A and B, nor does it detail the steps taken to arrive at the conclusion about C.