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animalsavior94

  • 4 years ago

find all the zeros of the function and write the function as a product of its linear factors. f(x)=3x^4 +2x^3 -28x^2 -14x+56

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  1. satellite73
    • 4 years ago
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    sure you typed it in right?

  2. animalsavior94
    • 4 years ago
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    no lol its f(x)=3x^4 +2x^3-29x^2-14x+56

  3. animalsavior94
    • 4 years ago
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    sorry

  4. satellite73
    • 4 years ago
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    good then cheat http://www.wolframalpha.com/input/?i=+f%28x%29%3D3x^4+%2B2x^3-29x^2-14x%2B56

  5. animalsavior94
    • 4 years ago
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    your supposed to do something else with it...i forgot whats it called but u gotta pull all the number out then find the zeros

  6. satellite73
    • 4 years ago
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    zeros are -2, 4/3, and +/- root 7

  7. satellite73
    • 4 years ago
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    factor. it is given to you in factored form. once you know -2 is a zero you factor as (x+2) something. you find the something by division

  8. animalsavior94
    • 4 years ago
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    ohh its synthetic divison could do show it by that

  9. satellite73
    • 4 years ago
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    i would hate to have to do this by hand.

  10. satellite73
    • 4 years ago
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    yes synthetic division list the coefficients. 3 2 -28 -14 56

  11. satellite73
    • 4 years ago
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    put a -2 on the side 3 2 -28 -14 56 -2 ______________________________________

  12. animalsavior94
    • 4 years ago
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    no its 3 2 -29 -14 56

  13. animalsavior94
    • 4 years ago
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    where did u get the -2 from the side from?

  14. satellite73
    • 4 years ago
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    bring down the three 3 2 -29 -14 56 -2 ______________________________________ 3

  15. animalsavior94
    • 4 years ago
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    no wait wheredid u get the -2 from

  16. satellite73
    • 4 years ago
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    3*-2=-6 3 2 -29 -14 56 -2 -6 ______________________________________ 3

  17. satellite73
    • 4 years ago
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    i got the -2 because i know -2 is a zero. you have to know that to begin with!

  18. satellite73
    • 4 years ago
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    2 + -6 = -4 3 2 -29 -14 56 -2 -6 ______________________________________ 3 -4

  19. animalsavior94
    • 4 years ago
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    wait ok this is what i did i got all the numbers i know what to do i just dont know where u got the -2 from

  20. satellite73
    • 4 years ago
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    -4*-2=8 3 2 -29 -14 56 -2 -6 8 ______________________________________ 3 -4

  21. satellite73
    • 4 years ago
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    in order to divide i must first know a zero of this function. if i do not i cannot divide. i am dividing by x + 2

  22. animalsavior94
    • 4 years ago
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    why?

  23. satellite73
    • 4 years ago
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    -29 + 8 = -21 3 2 -29 -14 56 -2 -6 8 ______________________________________ 3 -4 -21

  24. satellite73
    • 4 years ago
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    ok we know that f(-2)=0 so we know f factors as (x+2) q(x) we are trying to find q(x)

  25. satellite73
    • 4 years ago
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    we find q(x) by dividing f(x) by x + 2 which is what this synthetic division is doing

  26. satellite73
    • 4 years ago
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    if we do not know a zero we do not know what to divide by

  27. satellite73
    • 4 years ago
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    i know it is a zero because i cheated and used wolfram alpha. if i had to do it by hand i don't know what i would do. maybe graph it on a calculator and surmise that it crosses the x axis at -2

  28. satellite73
    • 4 years ago
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    the factored form of this beast is \[(x+2)(3x-4)(x^2 - 7)\]

  29. satellite73
    • 4 years ago
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    i am just factoring out the x + 2 at the moment.

  30. animalsavior94
    • 4 years ago
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    ohh i see

  31. animalsavior94
    • 4 years ago
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    ohh i see

  32. animalsavior94
    • 4 years ago
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    so what are the zeros if it ended with 3 -4 -21 28 0 ?

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