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lyzzy7

  • one year ago

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

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  1. lyzzy7
    • one year ago
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    @jim_thompson5910

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

  3. jim_thompson5910
    • one year ago
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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

  4. lyzzy7
    • one year ago
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    yes please @ParthKohli

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

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

  7. lyzzy7
    • one year ago
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    2

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

  9. lyzzy7
    • one year ago
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    yayyy :)

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

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

  12. ParthKohli
    • one year ago
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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.

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

  14. lyzzy7
    • one year ago
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    im confused @ParthKohli

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

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

  17. jim_thompson5910
    • one year ago
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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

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

  19. jim_thompson5910
    • one year ago
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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)

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

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

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

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

  24. lyzzy7
    • one year ago
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    ohh.

  25. jim_thompson5910
    • one year ago
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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)

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

  27. jim_thompson5910
    • one year ago
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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

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

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

  30. jim_thompson5910
    • one year ago
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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)

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

  32. jim_thompson5910
    • one year ago
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    sure go for it

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

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

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

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

  37. jim_thompson5910
    • one year ago
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    perfect

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

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

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

  41. jim_thompson5910
    • one year ago
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    you got it

  42. jim_thompson5910
    • one year ago
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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

  43. lyzzy7
    • one year ago
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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?

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

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

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

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

  48. lyzzy7
    • one year ago
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    like for the question

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

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

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

  52. jim_thompson5910
    • one year ago
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    so try again

  53. lyzzy7
    • one year ago
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    oops lol hold on

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

  55. jim_thompson5910
    • one year ago
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    good

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

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

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

  59. jim_thompson5910
    • one year ago
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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?

  60. lyzzy7
    • one year ago
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    g-6!

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

  62. lyzzy7
    • one year ago
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    :D

  63. jim_thompson5910
    • one year ago
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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

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

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

  66. jim_thompson5910
    • one year ago
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    that's great

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

  68. jim_thompson5910
    • one year ago
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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)

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

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

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

  72. lyzzy7
    • one year ago
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    2 and 10

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

  74. jim_thompson5910
    • one year ago
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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)

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

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

  77. jim_thompson5910
    • one year ago
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    correct

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

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

  80. lyzzy7
    • one year ago
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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?

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

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

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

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

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

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

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

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

  89. jim_thompson5910
    • one year ago
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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

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

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

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

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

  94. jim_thompson5910
    • one year ago
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    stop that

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

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

  97. lyzzy7
    • one year ago
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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.

  98. jim_thompson5910
    • one year ago
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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

  99. lyzzy7
    • one year ago
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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.

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

  101. jim_thompson5910
    • one year ago
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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)

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

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

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

  105. jim_thompson5910
    • one year ago
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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)?

  106. lyzzy7
    • one year ago
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    i guess so.

  107. jim_thompson5910
    • one year ago
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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.

  108. lyzzy7
    • one year ago
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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...

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

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

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

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

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

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

  115. lyzzy7
    • one year ago
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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.

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

  117. jim_thompson5910
    • one year ago
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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)

  118. lyzzy7
    • one year ago
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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.

  119. jim_thompson5910
    • one year ago
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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)

  120. jim_thompson5910
    • one year ago
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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

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

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

  123. jim_thompson5910
    • one year ago
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    correct

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

  125. jim_thompson5910
    • one year ago
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    sure thing

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

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

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

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

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

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

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

  133. jim_thompson5910
    • one year ago
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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)

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

  135. lyzzy7
    • one year ago
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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....

  136. jim_thompson5910
    • one year ago
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    lol magic

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

  138. lyzzy7
    • one year ago
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    yeah i did lol

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

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

  141. lyzzy7
    • one year ago
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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?

  142. jim_thompson5910
    • one year ago
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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)

  143. jim_thompson5910
    • one year ago
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    nice work

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

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

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

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

  148. jim_thompson5910
    • one year ago
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    yw

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

  150. lyzzy7
    • one year ago
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    youre*

  151. lyzzy7
    • one year ago
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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?

  152. jim_thompson5910
    • one year ago
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    but thanks lol

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

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

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

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

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

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

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