The wrong answer of the factorization of (x^6+x^3+1)

[2002Amrit]

Title: Inaccurate Polynomial Factorization in Brave Search AI

Hi Brave Community,

I’ve been using the AI assistant integrated into Brave Search and have encountered repeated inaccuracies in the polynomial factorization ( x^6 + x^3 + 1 ). Despite multiple attempts, the AI provided incorrect factorizations and failed to correctly verify the results. This has caused frustration and has impacted the reliability of the tool for my needs.

Details of the Issue

• Factor the polynomial ( x^6 + x^3 + 1 ).

Incorrect Responses:

• The AI provided the following incorrect factorization: [ x^6 + x^3 + 1 = (x^2 + x + 1)(x^4 - x^2 + 1) ]
• When verifying the factorization, the AI incorrectly combined terms and failed to simplify correctly, leading to: [ x^6 + x^5 - x^3 + x + 1 ]

Steps to Reproduce

1. Enter the query “Factor the polynomial ( x^6 + x^3 + 1 )” into the AI assistant.
2. Observe the provided factorization.
3. Verify the factorization by expanding the product of the factors.

Additional Notes

• The polynomial ( x^6 + x^3 + 1 ) is a known factorization problem, and the correct factors are well-documented in algebraic literature.
• The repeated incorrect responses and verification steps indicate a potential issue with the AI’s algebraic reasoning capabilities.

Suggested Improvements

• Enhance the AI’s ability to correctly factor polynomials and verify the results.
• Implement more robust verification steps to ensure the accuracy of the factorization.
• Consider adding more test cases and edge cases to the training data to improve the AI’s performance in algebraic problems.

Thank you for your attention to this matter. I look forward to seeing improvements in the AI’s performance.

Best regards,

[GREED]

[289wk]

Is “Factor the polynomial ( x^6 + x^3 + 1 )” the only search criteria that you have tried?

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I used a Windows OS 11 PC running Brave Browser v1.76.82. In a Brave Browser New Window, opened to:

• https://search.brave.com

I entered Factor the polynomial ( x^6 + x^3 + 1 ) into the Brave Search Engine’s Search Field, and then clicked on the AI button. Result:

That conclusion, again:

“For real number factorization, the polynomial remains as (x^6 + x^3 + 1) since it does not factor further into real polynomials of lower degree.”

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In the same search results page, there was a link to a math website tiger-algebra.com, where the answer to Factor the polynomial ( x^6 + x^3 + 1 ) or Factoring x^6 + x^3 + 1 is:

That [apparently NOT an AI] conclusion, again:

“Trinomial can not be factored.”

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Essentially, both results - for real numbers - is that, the polynomial cannot be factored.

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