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lyzzy7 Group Title

Which number makes this equation true? v^2 + 10v + 16 = (v + 8)(v + ?)

  • one year ago
  • one year ago

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  1. lyzzy7 Group Title
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    @jim_thompson5910

    • one year ago
  2. ParthKohli Group Title
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    I know a shortcut... can I say it?

    • one year ago
  3. jim_thompson5910 Group Title
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    if you were to set up a table, the lower right corner would have the value of 8*? where the answer would replace the question mark

    • one year ago
  4. lyzzy7 Group Title
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    yes please @ParthKohli

    • one year ago
  5. jim_thompson5910 Group Title
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    8*? has to equal 16 so basically 8p = 16 p = ???

    • one year ago
  6. jim_thompson5910 Group Title
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    where p is that answer

    • one year ago
  7. lyzzy7 Group Title
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    2

    • one year ago
  8. jim_thompson5910 Group Title
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    yep, you nailed it

    • one year ago
  9. lyzzy7 Group Title
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    yayyy :)

    • one year ago
  10. jim_thompson5910 Group Title
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    so v^2 + 10v + 16 = (v + 8)(v + ?) turns into v^2 + 10v + 16 = (v + 8)(v + 2)

    • one year ago
  11. lyzzy7 Group Title
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    What is the factored form of x^2 + 6x + 8?

    • one year ago
  12. ParthKohli Group Title
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    The shortcut says that in \(v^2 + \color{blue}{10}v + \rm something \) and \((v + \color{green}{a})(v + \color{green}{b})\), the sum of the greens is the blue guy.

    • one year ago
  13. jim_thompson5910 Group Title
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    find two numbers that a) multiply to 8 (last term) AND b) add to 6 (middle coefficient)

    • one year ago
  14. lyzzy7 Group Title
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    im confused @ParthKohli

    • one year ago
  15. lyzzy7 Group Title
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    2 and 4 . @jim_thompson5910

    • one year ago
  16. ParthKohli Group Title
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    It's simple. You have \((v + 8)(v + ?)\). This shortcut says that \(8 + ? = 10\).

    • one year ago
  17. jim_thompson5910 Group Title
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    So x^2 + 6x + 8 factors to (x+2)(x+4) The rule is that x^2 + bx + c factors to (x+m)(x+n) where m+n = b and m*n = c

    • one year ago
  18. lyzzy7 Group Title
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    ohhh! @ParthKohli thanks :)

    • one year ago
  19. jim_thompson5910 Group Title
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    So it's just a matter of finding those two numbers then writing it in the form (x+number1)(x+number2)

    • one year ago
  20. ParthKohli Group Title
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    I know that was sarcastic. -_-

    • one year ago
  21. lyzzy7 Group Title
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    hold on im thinking @jim_thompson5910

    • one year ago
  22. lyzzy7 Group Title
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    5 and 3?? @jim_thompson5910

    • one year ago
  23. jim_thompson5910 Group Title
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    you found the numbers already by saying 2 and 4 2+4 = 6 (middle coefficient) 2*4 = 8 (last term)

    • one year ago
  24. lyzzy7 Group Title
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    ohh.

    • one year ago
  25. jim_thompson5910 Group Title
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    so because you found two numbers that multiply to 8 AND add to 6 the factorization of x^2 + 6x + 8 would be (x+2)(x+4)

    • one year ago
  26. lyzzy7 Group Title
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    so it's (x + 4)(x + 2) ?

    • one year ago
  27. jim_thompson5910 Group Title
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    go ahead and expand out (x+2)(x+4) you'll find that you'll get x^2 + 6x + 8 back again

    • one year ago
  28. jim_thompson5910 Group Title
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    so essentially what you've done is gone in reverse of expanding (which was done in the previous problem)

    • one year ago
  29. lyzzy7 Group Title
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    i mostly get what you're saying. i have one more if you're willing to help?

    • one year ago
  30. jim_thompson5910 Group Title
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    correct, the order of the factors doesn't matter so (x+2)(x+4) is the same as (x+2)(x+4)

    • one year ago
  31. jim_thompson5910 Group Title
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    i meant (x+2)(x+4) is the same as (x+4)(x+2)

    • one year ago
  32. jim_thompson5910 Group Title
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    sure go for it

    • one year ago
  33. lyzzy7 Group Title
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    What is the factored form of x^2 – 7x + 12? and dont worry i knew what you meant lol

    • one year ago
  34. jim_thompson5910 Group Title
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    same idea, just different numbers

    • one year ago
  35. jim_thompson5910 Group Title
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    find two numbers that multiply to 12 AND add to -7

    • one year ago
  36. lyzzy7 Group Title
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    -3 and -4

    • one year ago
  37. jim_thompson5910 Group Title
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    perfect

    • one year ago
  38. jim_thompson5910 Group Title
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    so it factors to (x-3)(x-4)

    • one year ago
  39. lyzzy7 Group Title
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    (x – 4)(x – 3) ?

    • one year ago
  40. jim_thompson5910 Group Title
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    unfortunately this trick only works if the leading coefficient is 1, but it's still useful

    • one year ago
  41. jim_thompson5910 Group Title
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    you got it

    • one year ago
  42. jim_thompson5910 Group Title
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    that's the same as (x-3)(x-4) because the order of the factors does not matter ex: 2 time 3 = 6 and 3 times 2 = 6

    • one year ago
  43. lyzzy7 Group Title
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    okay i have a different kind of problem... The area of a garden is given by the trinomial g2 – 2g – 24. The garden’s length is g + 4. What is the garden’s width?

    • one year ago
  44. jim_thompson5910 Group Title
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    well it's actually the same type of problem, just worded differently

    • one year ago
  45. jim_thompson5910 Group Title
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    they want you to factor g^2 - 2g - 24

    • one year ago
  46. jim_thompson5910 Group Title
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    what do you get when you do?

    • one year ago
  47. lyzzy7 Group Title
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    write me an equation then and let me solve it :)

    • one year ago
  48. lyzzy7 Group Title
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    like for the question

    • one year ago
  49. jim_thompson5910 Group Title
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    find me two numbers that multiply to -24 and add to -2 at the same time

    • one year ago
  50. lyzzy7 Group Title
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    -6 and -4

    • one year ago
  51. jim_thompson5910 Group Title
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    -6 plus -4 = -10 and it does NOT equal -2

    • one year ago
  52. jim_thompson5910 Group Title
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    so try again

    • one year ago
  53. lyzzy7 Group Title
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    oops lol hold on

    • one year ago
  54. lyzzy7 Group Title
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    -6 and 4? -6*4= 24 -6+4 = -2 i think lol

    • one year ago
  55. jim_thompson5910 Group Title
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    good

    • one year ago
  56. jim_thompson5910 Group Title
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    So g^2 - 2g - 24 factors to (g-6)(g+4)

    • one year ago
  57. jim_thompson5910 Group Title
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    notice how g+4 is a factor

    • one year ago
  58. jim_thompson5910 Group Title
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    the other factor is g-6

    • one year ago
  59. jim_thompson5910 Group Title
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    let's go back to the question The area of a garden is given by the trinomial g2 – 2g – 24. The garden’s length is g + 4. What is the garden’s width?

    • one year ago
  60. lyzzy7 Group Title
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    g-6!

    • one year ago
  61. jim_thompson5910 Group Title
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    correct since Area = Length times Width

    • one year ago
  62. lyzzy7 Group Title
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    :D

    • one year ago
  63. jim_thompson5910 Group Title
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    so if you have some area expression and you factor it, you get (Length)*(Width) where length and width are the factors of the area

    • one year ago
  64. lyzzy7 Group Title
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    I actually get that!

    • one year ago
  65. jim_thompson5910 Group Title
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    it only works for rectangles though

    • one year ago
  66. jim_thompson5910 Group Title
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    that's great

    • one year ago
  67. lyzzy7 Group Title
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    hb this one? What is the factored form of 4x^2 + 12x + 5?

    • one year ago
  68. jim_thompson5910 Group Title
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    ok now the leading coefficient isn't 1 anymore, so we can't use that trick (well not the whole thing anyways)

    • one year ago
  69. jim_thompson5910 Group Title
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    but we can still use some of the trick

    • one year ago
  70. jim_thompson5910 Group Title
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    first multiply 4 (first coefficient) and 5 (last term) to get 4*5 = 20

    • one year ago
  71. jim_thompson5910 Group Title
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    now list two numbers that multiply to 20 AND add to 12 (middle coefficient)

    • one year ago
  72. lyzzy7 Group Title
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    2 and 10

    • one year ago
  73. lyzzy7 Group Title
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    is it (4x + 5)(x + 1) ?

    • one year ago
  74. jim_thompson5910 Group Title
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    so we break 12x into 2x + 10x then we factor by grouping 4x^2+12x+5 4x^2+2x+10x+5 (4x^2+2x)+(10x+5) 2x(2x+1)+(10x+5) 2x(2x+1)+5(2x+1) (2x+5)(2x+1)

    • one year ago
  75. jim_thompson5910 Group Title
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    hopefully factoring by grouping is a familiar term

    • one year ago
  76. lyzzy7 Group Title
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    so the final answer is (2x + 1)(2x + 5), right?

    • one year ago
  77. jim_thompson5910 Group Title
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    correct

    • one year ago
  78. jim_thompson5910 Group Title
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    hopefully you see how I got all that

    • one year ago
  79. lyzzy7 Group Title
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    okay, thanks :D and lol yeah mostly.

    • one year ago
  80. lyzzy7 Group Title
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    The area of a rectangular swimming pool is 10x2 – 19x – 15. The length of the pool is 5x + 3. What is the width of the pool?

    • one year ago
  81. jim_thompson5910 Group Title
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    alright, just keep practicing and it'll make more sense

    • one year ago
  82. jim_thompson5910 Group Title
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    10*(-15) = -150

    • one year ago
  83. jim_thompson5910 Group Title
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    find two numbers that multiply to -150 and they add to -19

    • one year ago
  84. lyzzy7 Group Title
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    why do you multiply 10 and -15?

    • one year ago
  85. jim_thompson5910 Group Title
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    because I'm using the AC method for factoring this method starts out by multiplying the first and last coefficients

    • one year ago
  86. jim_thompson5910 Group Title
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    then you find two numbers that multiply to that result and add to the middle number

    • one year ago
  87. lyzzy7 Group Title
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    so the formula is ax^2 + bx + c right?

    • one year ago
  88. jim_thompson5910 Group Title
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    that's a basic form of a quadratic, yes

    • one year ago
  89. jim_thompson5910 Group Title
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    you would multiply 'a' and 'c' to get a*c or just ac then you find two numbers that multiply to ac and add to b

    • one year ago
  90. jim_thompson5910 Group Title
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    so that's why they call it the ac method

    • one year ago
  91. lyzzy7 Group Title
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    I cant find the two numbers that multiply to -150 and add to -19..

    • one year ago
  92. lyzzy7 Group Title
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    im too dumb..

    • one year ago
  93. jim_thompson5910 Group Title
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    no you're not

    • one year ago
  94. jim_thompson5910 Group Title
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    stop that

    • one year ago
  95. jim_thompson5910 Group Title
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    there's a long list to check, but luckily there's a shortcut

    • one year ago
  96. jim_thompson5910 Group Title
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    have you heard of the quadratic formula before?

    • one year ago
  97. lyzzy7 Group Title
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    noo. my teacher sucks this year. she is retiring so she doesnt teach us anything useful, she just assigns stuff and tells us to read our book to figure out how to do it, but the book has no tips or tricks.

    • one year ago
  98. jim_thompson5910 Group Title
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    ah i'm sry to hear that, at least she'll be gone and a (hopefully) better teacher will take over

    • one year ago
  99. lyzzy7 Group Title
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    yeah im going to a private school next year, sadly now i need to get a second job because its $6,000 a year.

    • one year ago
  100. jim_thompson5910 Group Title
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    dang that's quite pricey

    • one year ago
  101. jim_thompson5910 Group Title
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    well anyways, the quadratic formula isn't that bad to learn (it's a bit ugly the first time you see it, but once you get used to it, it's not so bad)

    • one year ago
  102. lyzzy7 Group Title
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    i know right, and okay shoot

    • one year ago
  103. jim_thompson5910 Group Title
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    the quadratic formula is \[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\] does that formula look familiar?

    • one year ago
  104. lyzzy7 Group Title
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    noo.......

    • one year ago
  105. jim_thompson5910 Group Title
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    ok but does it look readable by that I mean, could you simplify that formula if you had to (or if you had to plug in numbers for a, b, and c)?

    • one year ago
  106. lyzzy7 Group Title
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    i guess so.

    • one year ago
  107. jim_thompson5910 Group Title
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    ok in this case, a = 10, b = -19 and c = -15 we plug those values into the formula to get this (there's a lot of steps, but just take things one step at a time) \[\Large x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\] \[\Large x = \frac{-(-19)\pm\sqrt{(-19)^2-4(10)(-15)}}{2(10)}\] \[\Large x = \frac{19\pm\sqrt{361-(-600)}}{20}\] \[\Large x = \frac{19\pm\sqrt{361+600}}{20}\] \[\Large x = \frac{19\pm\sqrt{961}}{20}\] \[\Large x = \frac{19+\sqrt{961}}{20} \ \text{or} \ x = \frac{19-\sqrt{961}}{20}\] \[\Large x = \frac{19+31}{20} \ \text{or} \ x = \frac{19-31}{20}\] \[\Large x = \frac{50}{20} \ \text{or} \ x = \frac{-12}{20}\] \[\Large x = \frac{5}{2} \ \text{or} \ x = -\frac{3}{5}\] Let me know when you want to continue.

    • one year ago
  108. lyzzy7 Group Title
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    I honestly have no clue what any of that is. att all. like at all. im taking algebra 1 btw. im in 8th grade. but i really have cant even read that...

    • one year ago
  109. lyzzy7 Group Title
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    like i cant even read it in my head let alone get it. i have a headache.

    • one year ago
  110. lyzzy7 Group Title
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    fml. i hate math.

    • one year ago
  111. jim_thompson5910 Group Title
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    alright, sorry jumped too far ahead

    • one year ago
  112. lyzzy7 Group Title
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    its not your fault. it just is ridiculous that something that complicated even exists. i hate this world.

    • one year ago
  113. jim_thompson5910 Group Title
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    well much more complicated things exist (that even I don't understand), but that's what keeps things interesting

    • one year ago
  114. jim_thompson5910 Group Title
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    let's ignore the quadratic formula until you get more practice with it

    • one year ago
  115. lyzzy7 Group Title
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    soo what is the answer to this? The area of a rectangular swimming pool is 10x2 – 19x – 15. The length of the pool is 5x + 3. What is the width of the pool? its like 5 am where i live and i still havent slept.

    • one year ago
  116. jim_thompson5910 Group Title
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    why not sleep then come back?

    • one year ago
  117. jim_thompson5910 Group Title
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    10(-15) = -150 find two numbers that multiply to -150 and add to -19 ....do a bunch of trial and error guesses... you'll find that the two numbers are 6 and -25 So this means... 10x^2-19x-15 10x^2+6x-25x-15 (10x^2+6x)+(-25x-15) 2x(5x+3)+(-25x-15) 2x(5x+3)-5(5x+3) (2x-5)(5x+3) --------------------------------------------------------------------------- In short 10x^2-19x-15 completely factors to (2x-5)(5x+3)

    • one year ago
  118. lyzzy7 Group Title
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    because the kind of person i am, when i have something on my mind, i have to get it done before i'd ever care for myself.

    • one year ago
  119. jim_thompson5910 Group Title
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    i gotcha, that's both a good and bad trait because yes it's good to be this motivated, but not when you're sleep deprived (you won't learn much without a good night's sleep)

    • one year ago
  120. jim_thompson5910 Group Title
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    so anyways, back to the problem above I showed how 10x^2-19x-15 factors to (2x-5)(5x+3) 5x+3 was one factor we were already given, 2x-5 is the other one So the width is 2x-5

    • one year ago
  121. lyzzy7 Group Title
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    Got it. and the length is 5x+3 right?

    • one year ago
  122. jim_thompson5910 Group Title
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    so length = 5x + 3 (given) width = 2x - 5 (just found this)

    • one year ago
  123. jim_thompson5910 Group Title
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    correct

    • one year ago
  124. lyzzy7 Group Title
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    ughhh now i have to solve two more, then ima sleep. thank you so much for the help!

    • one year ago
  125. jim_thompson5910 Group Title
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    sure thing

    • one year ago
  126. jim_thompson5910 Group Title
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    go ahead and post and hopefully it won't take too long

    • one year ago
  127. jim_thompson5910 Group Title
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    then you can finally sleep (til you have to get up in the morning...ugh lol)

    • one year ago
  128. lyzzy7 Group Title
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    you sure? i mean i could try to do them on my own if you want.

    • one year ago
  129. jim_thompson5910 Group Title
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    sure whatever works best for you

    • one year ago
  130. jim_thompson5910 Group Title
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    how about you work them and I check what you get

    • one year ago
  131. jim_thompson5910 Group Title
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    or I can show you how if you're stuck

    • one year ago
  132. lyzzy7 Group Title
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    alright heres this one What is the factored form of 2x2 + x – 3? then i'll do the other.

    • one year ago
  133. jim_thompson5910 Group Title
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    ok 2(3) = -6 find two numbers that multiply to -6 and add to 1 those two numbers are 3 and -2 so... 2x^2+x-3 2x^2+3x-2x-3 ... break 1x into 3x - 2x, then factor by grouping (2x^2+3x)+(-2x-3) x(2x+3)+(-2x-3) x(2x+3)-1(2x+3) (x-1)(2x+3) ------------------------------------- 2x^2+x-3 completely factors to (x-1)(2x+3)

    • one year ago
  134. jim_thompson5910 Group Title
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    hopefully I didn't cut you off there?

    • one year ago
  135. lyzzy7 Group Title
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    no you're good, i was just going to say the two numbers. but how in god's name did you do that so fast....

    • one year ago
  136. jim_thompson5910 Group Title
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    lol magic

    • one year ago
  137. jim_thompson5910 Group Title
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    ah i should have let you say the two numbers, but hopefully you got 3 and -2 ?

    • one year ago
  138. lyzzy7 Group Title
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    yeah i did lol

    • one year ago
  139. jim_thompson5910 Group Title
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    ok perfect, you'll be a pro in no time

    • one year ago
  140. jim_thompson5910 Group Title
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    you just need to practice more with factoring by grouping (and the quadratic formula when you get more time)

    • one year ago
  141. lyzzy7 Group Title
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    and for the other one it was What is the factored form of 3x2 + 21x – 24? and i got 3(x + 8)(x – 1) am i almost right?

    • one year ago
  142. jim_thompson5910 Group Title
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    no, you're not almost right....you're absolutely correct (lol I wanted to sound like a game show host for a sec)

    • one year ago
  143. jim_thompson5910 Group Title
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    nice work

    • one year ago
  144. lyzzy7 Group Title
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    OMG YAY:))) Thank you sooo much! like i really didnt get half my stuff till you helped lol

    • one year ago
  145. jim_thompson5910 Group Title
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    glad to be of help, now get some sleep lol

    • one year ago
  146. lyzzy7 Group Title
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    will do, thank you :)

    • one year ago
  147. jim_thompson5910 Group Title
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    I know, I probably sound like your mom, but idc lol

    • one year ago
  148. jim_thompson5910 Group Title
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    yw

    • one year ago
  149. lyzzy7 Group Title
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    your good lol! how old are u by the way?

    • one year ago
  150. lyzzy7 Group Title
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    youre*

    • one year ago
  151. lyzzy7 Group Title
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    lol nah its cool. and its amazing that you put your brain to help people. what do you do as a job?

    • one year ago
  152. jim_thompson5910 Group Title
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    but thanks lol

    • one year ago
  153. lyzzy7 Group Title
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    i hope you go far! honestly

    • one year ago
  154. jim_thompson5910 Group Title
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    thanks, i hope so too

    • one year ago
  155. jim_thompson5910 Group Title
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    definitely getting a lot of practice here lol

    • one year ago
  156. lyzzy7 Group Title
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    lol, there ya go!

    • one year ago
  157. jim_thompson5910 Group Title
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    and building networks as well (well sorta i guess)

    • one year ago
  158. jim_thompson5910 Group Title
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    so that's another plus

    • one year ago
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