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calculusxy

  • one year ago

factoring quadratic expression...

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  1. calculusxy
    • one year ago
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    \[\huge 12x^2 + 12x + 3\]

  2. calculusxy
    • one year ago
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    @Nnesha @hartnn

  3. Rizags
    • one year ago
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    factor out a 3 first

  4. calculusxy
    • one year ago
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    \[\large 3(4x^2 + 4x + 1) \]

  5. Rizags
    • one year ago
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    Then you'll notice something about the resulting quadratic

  6. Rizags
    • one year ago
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    hint: \[(a+b)^2 = a^2+2ab+b^2\]

  7. calculusxy
    • one year ago
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    i still don't understand

  8. Rizags
    • one year ago
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    using my model, let\[\large a=2x\] and \[\large b=1\]

  9. calculusxy
    • one year ago
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    ok

  10. calculusxy
    • one year ago
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    can you please get to the point?

  11. Rizags
    • one year ago
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    ok, then \[12x^2+12x+3 = 3(2x+1)^2\]

  12. Nnesha
    • one year ago
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    there are like 4+ ways to factor quadratic equation i like AC method where we find two numbers when we multiply them we should get product of AC (a=leading coefficient , C= constant ) and when we add them we should get middle term which is b \[\rm Ax^2+Bx+C\] a=leading coefficient b=middle term c-constant

  13. Nnesha
    • one year ago
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    |dw:1444168815625:dw| multiply A times C what two numbers you should multiply to get 4 and when you add them you should get 4

  14. calculusxy
    • one year ago
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    36: 1, 2, 3, 4, 6, 9, 12, 18, 36

  15. Nnesha
    • one year ago
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    first step)take out the GCF so 3( 4x^2+4x+1) is correct

  16. Nnesha
    • one year ago
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    \[3 \color{ReD}{(4x^2+4x+1)}\] now we factor the quadratic equation 4x^2+4x+1

  17. calculusxy
    • one year ago
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    how do we factor that?

  18. Nnesha
    • one year ago
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    how do you want to factor it ? you can use quadratic formula or AC method i posted above

  19. calculusxy
    • one year ago
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    ac

  20. Nnesha
    • one year ago
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    alright read my comments let me know if you have a question :=)

  21. calculusxy
    • one year ago
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    i multiplied 4 x 1 = 4 factors of 4: 1, 2, 4

  22. Nnesha
    • one year ago
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    4 times 1 = 4 now what two numbers add up to 4 and when u multiply them you should get 4

  23. calculusxy
    • one year ago
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    3(2x + 1)(2x + 1)

  24. Nnesha
    • one year ago
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    hmm well in this question AC=4 and b=4 so two numbers are 2 times 2 =4 2+2= 4 and bec leading isn't equal to one we should factor by grouping |dw:1444169462918:dw| keep the first and last term write both numbers in the middle

  25. Nnesha
    • one year ago
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    can you please how u got 2x+1 ?? :=)

  26. Nnesha
    • one year ago
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    explain*

  27. calculusxy
    • one year ago
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    |dw:1444169574708:dw|

  28. Nnesha
    • one year ago
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    perfect!!!

  29. calculusxy
    • one year ago
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    and then i carried down the 3

  30. calculusxy
    • one year ago
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    |dw:1444169772616:dw|

  31. Nnesha
    • one year ago
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    |dw:1444169756892:dw| forgot the positive sign

  32. Nnesha
    • one year ago
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    yes right

  33. calculusxy
    • one year ago
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    okay thanks!

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