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ParthKohli

  • 2 years ago

factoring

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  1. ParthKohli
    • 2 years ago
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    Should I use \(a^3 + b^3 = (a + b)(a^2 - ab+b^2)\)?

  2. ParthKohli
    • 2 years ago
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    Or am I complicating it?

  3. drawar
    • 2 years ago
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    The factorization is not that easy to find

  4. ParthKohli
    • 2 years ago
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    Yeah, but Wolfram does give a simple solution.

  5. drawar
    • 2 years ago
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    Why simple? Complex numbers join the party and you can't even find a real root to get started...

  6. ParthKohli
    • 2 years ago
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    Yeah, but the solution is simple. :-P This is 9th grade math... I don't know why I'm not able to do this one

  7. drawar
    • 2 years ago
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    Gimme a minute...

  8. drawar
    • 2 years ago
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    \[\begin{array}{l} 9{x^4} + 9{x^3} + 8{x^2} + 9x + 9 = 0 \\ 9({x^4} + {x^3} + 2{x^2} + x + 1) = 10{x^2} \\ 9{({x^2} + 1)^2} + 9x({x^2} + 1) - 10{x^2} = 0 \\ {\left( {3({x^2} + 1)} \right)^2} + \left( {3({x^2} + 1)} \right)(3x) - 10{x^2} = 0 \\ {\left( {3({x^2} + 1)} \right)^2} - \left( {3({x^2} + 1)} \right)(2x) + \left( {3({x^2} + 1)} \right)(5x) - (2x)(5x) = 0 \\ \end{array}\] Actually 4 mins already, and I left out the last step :P

  9. ParthKohli
    • 2 years ago
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    Ha, but how did you choose to add \(10x^2\) to both sides? Doesn't it seem arbitrary?

  10. drawar
    • 2 years ago
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    No it does not. At first glance I was going to add x^2 only, but then to complete the square I have to add another 9x^2

  11. ParthKohli
    • 2 years ago
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    How do you complete the square in a polynomial with degree 3 or higher? :-O

  12. ParthKohli
    • 2 years ago
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    Oh lol

  13. ParthKohli
    • 2 years ago
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    Got it

  14. ParthKohli
    • 2 years ago
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    \[(3x)^2 + (3)^2\]has the middle term \(2(3x)^2 (3)^2 = 18x^2\). Thanks :-)

  15. drawar
    • 2 years ago
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    just pick the dominant term with even degree and add/subtract until you have a complete square

  16. mathslover
    • 2 years ago
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    KUDOS FOR DRAWAR , GREAT WORK MR. DRAWAR :)

  17. drawar
    • 2 years ago
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    Thanks for that @mathslover :) Oh kids have to study so many things nowadays...

  18. ParthKohli
    • 2 years ago
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    @drawar Can you send me the link where you learnt how to do this?

  19. drawar
    • 2 years ago
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    Sorry I don't have any link to share here, just do more practice and you'll eventually get the hang of it!

  20. ParthKohli
    • 2 years ago
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    OK :-|

  21. drawar
    • 2 years ago
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    Just out of curiosity, are you a 9th grader?

  22. ParthKohli
    • 2 years ago
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    Yes.

  23. ParthKohli
    • 2 years ago
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    Just started 9th grade.

  24. drawar
    • 2 years ago
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    Nice, all the best with your study then!

  25. ParthKohli
    • 2 years ago
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    Thanks!

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