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anonymous

  • one year ago

FACTORING! please help me factor x^2+3x+9/4

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  1. anonymous
    • one year ago
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    @jagr2713

  2. myininaya
    • one year ago
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    hint: this may help" \[x^2+bx+\frac{c}{a} \\ \frac{1}{a}(ax^2+bax+\frac{c(a)}{a}) \\ \frac{1}{a}(ax^2+bax+c)\]

  3. anonymous
    • one year ago
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    ok so my equation should look like \[1/4(4x^2+3(4)x+9)\]

  4. myininaya
    • one year ago
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    yep it is like dividing everything by 4 at the same time as multiplying everything by 4 and we know 4/4=1 so yep

  5. myininaya
    • one year ago
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    and 3(4) can be written as 12 of course

  6. myininaya
    • one year ago
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    you can also see if you need to factor anymore

  7. anonymous
    • one year ago
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    right, so now my equation should be \[x^2+12+9\]

  8. myininaya
    • one year ago
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    well you are missing 1/4( ) and a 4 in front of x^2 and a x next to the 12

  9. myininaya
    • one year ago
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    \[\frac{1}{4}(4x^2+12x+9)\]

  10. myininaya
    • one year ago
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    anyways let's look at the thing in ( )

  11. myininaya
    • one year ago
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    can you find two numbers that multiply to be 4(9)=36 and add up to be 12

  12. anonymous
    • one year ago
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    something that are multiples to 36 and add to 12?

  13. myininaya
    • one year ago
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    yep

  14. anonymous
    • one year ago
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    6 and 6

  15. myininaya
    • one year ago
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    yes yes! :)

  16. myininaya
    • one year ago
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    \[\frac{1}{4}(4x^2+6x+6x+9)\] now we can ignore the 1/4 and bring it down later but we need to factor the thing inside the ( )by grouping

  17. myininaya
    • one year ago
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    we will bring the 1/4 down later \[4x^2+6x+6x+9 \\ (4x^2+6x)+(6x+9) \\ 2x(2x+3)+(6x+9)\] you try factoring the 6x+9

  18. anonymous
    • one year ago
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    (6x+9) will equal 3x(2x+3)

  19. myininaya
    • one year ago
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    well 9 doesn't have a factor of x so you cannot factor an x out of it unless you divide by x but that is making is nastier than it should be 6x+9=3(2x+3)

  20. myininaya
    • one year ago
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    we will bring down 1/4 later \[2x(2x+3)+3(2x+3)\] now one last step

  21. anonymous
    • one year ago
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    oh ok, that makes sense!

  22. anonymous
    • one year ago
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    I'm not sure how to do the last step

  23. myininaya
    • one year ago
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    example to factor a(b+c)+m(b+c) notice both terms both a(b+c) and m(b+c) have the common factor (b+c) so I can factor (b+c) out of both terms in the sum (b+c)(a+m)

  24. myininaya
    • one year ago
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    so you see (2x+3) in both terms the terms being 2x(2x+3) and 3(2x+3)

  25. myininaya
    • one year ago
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    what is left of the first term when factoring out the (2x+3) is 2x and of the second term is +3

  26. myininaya
    • one year ago
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    2x(2x+3)+3(2x+3) (2x+3)(2x+3)

  27. myininaya
    • one year ago
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    don't forget to bring down the 1/4

  28. anonymous
    • one year ago
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    so its just 1/4(2x+3)(2x+3)

  29. myininaya
    • one year ago
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    or 1/4(2x+3)^2

  30. myininaya
    • one year ago
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    or...

  31. myininaya
    • one year ago
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    \[\frac{1}{4}(2x+3)^2 \\ \frac{1}{2^2}(2x+3)^2 \\ \frac{1^2}{2^2}(2x+3)^2 \\ (\frac{1}{2}(2x+3))^2 \\ (\frac{2x+3}{2})^2 \] there is another or :p

  32. myininaya
    • one year ago
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    you could separate the fraction inside the ( )^2

  33. myininaya
    • one year ago
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    but anyways yeah you are done

  34. anonymous
    • one year ago
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    so its just \[(x+\frac{ 3 }{ 2 })^2\]

  35. myininaya
    • one year ago
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    yep

  36. anonymous
    • one year ago
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    Thank you so much, I really appreciate your help!

  37. myininaya
    • one year ago
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    if we would have noticed the following to begin with: \[x^2+3x+(\frac{3}{2})^2=(x+\frac{3}{2})^2 \] we wouldn't had so much work

  38. myininaya
    • one year ago
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    \[x^2+kx+(\frac{k}{2})^2=(x+\frac{k}{2})^2 \]

  39. anonymous
    • one year ago
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    oh yes! That's very true, we missed that. Oh well :)

  40. myininaya
    • one year ago
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    for example: \[x^2+5x+(\frac{5}{2})^2=(x+\frac{5}{2})^2 \\ x^2-5x+(\frac{5}{2})^2=(x-\frac{5}{2})^2 \\ x^2-3x+(\frac{-3}{2})^2=(x-\frac{3}{2})^2 \\ x^2-2x+(\frac{-2}{2})^2=(x-1)^2 \]

  41. anonymous
    • one year ago
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    that actually makes perfect sense, thank you so much for showing me that formula! It's a lot easier than all the other ways I have been taught.

  42. myininaya
    • one year ago
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    no problem :)

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