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anonymous

  • 5 years ago

12ax^3+20bx^2+32cx what does this equal when factored out??

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  1. anonymous
    • 5 years ago
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    What factors do all 3 terms have in common?

  2. anonymous
    • 5 years ago
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    i dotn know none of tis makes any sense because my teacher doesnt teach any of the material he just throws the assighnmkent and tests in your face and expect you to know what to do

  3. anonymous
    • 5 years ago
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    Ok, do you know what I mean by terms?

  4. anonymous
    • 5 years ago
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    How many terms does the expression you gave have?

  5. anonymous
    • 5 years ago
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    3

  6. anonymous
    • 5 years ago
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    Right. Ok so lets look at the first term \[12ax^3\] That's saying \(12 \times a \times x^3\) right?

  7. anonymous
    • 5 years ago
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    yeah

  8. anonymous
    • 5 years ago
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    Ok, so 12, a, and \(x^3\) are factors of \(12ax^3\). But some of those can be factored further. 12 for example can be factored into what?

  9. anonymous
    • 5 years ago
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    i dotn even know what factors are so yeah

  10. anonymous
    • 5 years ago
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    Ok. Factors are like terms, but terms are for addition and subtraction. Factors are for multiplication and division. When I say \(3 \times 4\) = 12, I'm saying that 12 is the PRODUCT of the FACTORS 4 and 3.

  11. anonymous
    • 5 years ago
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    So what are the different things you can multiply to get 12?

  12. anonymous
    • 5 years ago
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    4 and 3 and 1 and 12

  13. anonymous
    • 5 years ago
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    4*3, 1*12, and 6*2 right?

  14. anonymous
    • 5 years ago
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    yeah

  15. anonymous
    • 5 years ago
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    We will ignore the factorization using 1's because you can have infinitely many 1's when you factor something, it's not very useful. 12*1 = 12, but 12*1*1*1*1*1 = 12 also.

  16. anonymous
    • 5 years ago
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    So lets look at the other 2 sets of factors. 4 and 3.

  17. anonymous
    • 5 years ago
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    Err 4*3 and 6*2

  18. anonymous
    • 5 years ago
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    Starting with 4*3. Now can either of those factors be factored further?

  19. anonymous
    • 5 years ago
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    Remember to ignore factorizations that use a 1.

  20. anonymous
    • 5 years ago
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    the 4

  21. anonymous
    • 5 years ago
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    And its factors are?

  22. anonymous
    • 5 years ago
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    2*2

  23. anonymous
    • 5 years ago
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    Right. So putting it all together we have that 12 = 2*2*3

  24. anonymous
    • 5 years ago
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    And if we factor the other way 12 = 6*2 = (3*2)*2 We get the same thing 2*2*3

  25. anonymous
    • 5 years ago
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    So no matter how you factor something you will end up with the same factors.

  26. anonymous
    • 5 years ago
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    So we can say that 12 has two factors of 2. And one factor of 3.

  27. anonymous
    • 5 years ago
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    ok

  28. anonymous
    • 5 years ago
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    Now then, what are the factors of \(x^2\)

  29. anonymous
    • 5 years ago
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    Remember that \(x^2\) = x*x

  30. anonymous
    • 5 years ago
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    x isnt a number so it doesnt have factors

  31. anonymous
    • 5 years ago
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    It is a number. We just don't know what number it is. So we can't factor further than x, but we do know that \(x^2\) has two factors of x.

  32. anonymous
    • 5 years ago
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    right? Because \(x*x = x^2\)

  33. anonymous
    • 5 years ago
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    yeah

  34. anonymous
    • 5 years ago
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    Ok and a cannot be factored further cause we don't know what number it is either.

  35. anonymous
    • 5 years ago
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    Ok, so now putting it all together we have that \(12ax^2\) has two factors of 2, one factor of 3, one factor of a, and two factors of x.

  36. anonymous
    • 5 years ago
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    ok

  37. anonymous
    • 5 years ago
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    Whoops, it should be \(12ax^3\). So that's 3 factors of x

  38. anonymous
    • 5 years ago
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    So now you try to do the second term.

  39. anonymous
    • 5 years ago
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    2*10 2*5

  40. anonymous
    • 5 years ago
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    2*10 2*5

  41. anonymous
    • 5 years ago
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    20 = 2*10 = 2*(2*5) Is that what you mean?

  42. anonymous
    • 5 years ago
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    it is now

  43. anonymous
    • 5 years ago
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    Ok, so what are the factors of \(20bx^2\)

  44. anonymous
    • 5 years ago
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    list them just like I did for \(12ax^3\)

  45. anonymous
    • 5 years ago
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    2*5 b x*x

  46. anonymous
    • 5 years ago
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    You're missing an extra factor of 2.

  47. anonymous
    • 5 years ago
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    5*2 = 10, not 20

  48. anonymous
    • 5 years ago
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    5*2*2 = 20

  49. anonymous
    • 5 years ago
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    Try it again with the 3rd term just to be sure you have it down.

  50. anonymous
    • 5 years ago
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    i dont know anything for 32 other than 32 and 1

  51. anonymous
    • 5 years ago
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    Well it's an even number right?

  52. anonymous
    • 5 years ago
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    So you know at least that it has a factor of 2.

  53. anonymous
    • 5 years ago
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    yeah

  54. anonymous
    • 5 years ago
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    So what times 2 is 32?

  55. anonymous
    • 5 years ago
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    And if you aren't sure, how can you find out?

  56. anonymous
    • 5 years ago
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    If 2*h = 32 then h = 32/2 right?

  57. anonymous
    • 5 years ago
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    sorry my computetr is being extremely tarded and its pissing me off but its 16

  58. anonymous
    • 5 years ago
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    sorry my computetr is being extremely tarded and its pissing me off but its 16

  59. anonymous
    • 5 years ago
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    Ok right. And what are the factors of 16?

  60. anonymous
    • 5 years ago
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    2*8

  61. anonymous
    • 5 years ago
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    And the factors of 8?

  62. anonymous
    • 5 years ago
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    2*4

  63. anonymous
    • 5 years ago
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    And 4 can be factored

  64. anonymous
    • 5 years ago
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    2*2

  65. anonymous
    • 5 years ago
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    Ok let me show you a trick for keeping track of all this stuff.

  66. anonymous
    • 5 years ago
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    http://www.dabbleboard.com/draw?b=Guest666631&i=0&c=3653c1e6f8130c42c19163377ccd7be35dcb8560

  67. anonymous
    • 5 years ago
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    my computer keeps fluttering up and its pissing me off so i g2g

  68. anonymous
    • 5 years ago
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    ok

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