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tootsi123

  • one year ago

Which of the following is polynomial factor of 8x^2+22x-6? A (4x-3) B (4x+3) C (8x-2) D (8x+3) E (8x+6)

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  1. tootsi123
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    what is the GCF of 8,22, and 6 ?

  3. tootsi123
    • one year ago
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    Oh wait i think i get it hold on... 8= 2^3 22=2*11 6=2*3

  4. tootsi123
    • one year ago
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    is that right so far??

  5. jim_thompson5910
    • one year ago
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    notice how 2 is a factor in each, so we can factor out 2 8x^2+22x-6 = 2(4x^2+11x - 3)

  6. jim_thompson5910
    • one year ago
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    how would we factor 4x^2+11x - 3 ?

  7. tootsi123
    • one year ago
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    Wouldn't you start simplifying the problem?

  8. jim_thompson5910
    • one year ago
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    multiply the first coefficient (4) and the last term (-3) 4*(-3) = -12 what two factors of -12 add to 11 ?

  9. jim_thompson5910
    • one year ago
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    put another way: what two numbers multiply to -12 and add to 11?

  10. tootsi123
    • one year ago
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    Wait i am confused... i thought you couldn't combine terms unless they were like terms.... and would 3 be one

  11. jim_thompson5910
    • one year ago
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    I'm not combining like terms

  12. jim_thompson5910
    • one year ago
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    I'm asking for the two numbers because it will help factor

  13. tootsi123
    • one year ago
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    oh. Okay so 11 is a prime number so its only factor is one.

  14. tootsi123
    • one year ago
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    -12 could be 6,2,3,4

  15. jim_thompson5910
    • one year ago
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    here are all of the ways to multiply two whole numbers to get -12 -1*12 -2*6 -3*4 -4*3 -6*2 -12*1 which pair of factors will add up to 11?

  16. tootsi123
    • one year ago
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    The first one

  17. jim_thompson5910
    • one year ago
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    yep -1*12 = -12 -1 + 12 = 11

  18. jim_thompson5910
    • one year ago
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    so we can break up the 11x into -1x + 12x

  19. tootsi123
    • one year ago
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    Oh okay...

  20. jim_thompson5910
    • one year ago
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    4x^2+11x - 3 4x^2-1x + 12x - 3

  21. jim_thompson5910
    • one year ago
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    then we'd factor 4x^2-1x + 12x - 3 by grouping

  22. jim_thompson5910
    • one year ago
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    group up the terms in pairs 4x^2-1x + 12x - 3 (4x^2-1x) + (12x - 3) do you see what step is next?

  23. tootsi123
    • one year ago
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    Simplify them.

  24. jim_thompson5910
    • one year ago
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    specifically you factor each group

  25. jim_thompson5910
    • one year ago
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    how can you factor 4x^2-1x ?

  26. tootsi123
    • one year ago
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    I don't know?

  27. jim_thompson5910
    • one year ago
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    we can factor out x, agreed? 4x^2 - 1x = x(4x - 1)

  28. tootsi123
    • one year ago
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    oh yeah since they are like terms

  29. jim_thompson5910
    • one year ago
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    how would you factor 12x - 3 ?

  30. tootsi123
    • one year ago
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    Wouldn't you just do 12 -3 and then add the x

  31. jim_thompson5910
    • one year ago
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    what factors do 12 and 3 have in common?

  32. jim_thompson5910
    • one year ago
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    12x and -3 aren't like terms

  33. tootsi123
    • one year ago
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    oh duh 3

  34. jim_thompson5910
    • one year ago
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    yeah so 12x - 3 = 3(4x - 1)

  35. jim_thompson5910
    • one year ago
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    4x^2-1x + 12x - 3 (4x^2-1x) + (12x - 3) x(4x - 1) + 3(4x - 1)

  36. jim_thompson5910
    • one year ago
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    what factor shows up twice?

  37. tootsi123
    • one year ago
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    one

  38. jim_thompson5910
    • one year ago
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    what else

  39. tootsi123
    • one year ago
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    4

  40. jim_thompson5910
    • one year ago
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    the 4x-1 shows up twice

  41. jim_thompson5910
    • one year ago
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    we can factor that out x(4x - 1) + 3(4x - 1) will turn into (x+3)(4x - 1)

  42. jim_thompson5910
    • one year ago
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    so hopefully you see how 8x^2+22x-6 factors to 2(x+3)(4x - 1)

  43. tootsi123
    • one year ago
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    I think so

  44. jim_thompson5910
    • one year ago
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    go over the steps a few times to make sure you have a solid grasp of it. you can ask questions if you aren't sure about a step or two

  45. tootsi123
    • one year ago
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    Okay

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