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monroe17

  • 2 years ago

((x^2+3x+4)-2) simplifies to -2x^2-6x-8

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  1. monroe17
    • 2 years ago
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    fog.. when f(x)=x-2 g(x)=x^2+3x+4 =((x^2+3x+4)-2) = -2x^2-6x-8

  2. jim_thompson5910
    • 2 years ago
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    f(x)=x-2 f(g(x))=g(x)-2 f(g(x))=x^2+3x+4-2 f(g(x))=x^2+3x+2

  3. jim_thompson5910
    • 2 years ago
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    You're not multiplying, you're subtracting in this case

  4. monroe17
    • 2 years ago
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    oh.. so I don't distribute the -2?

  5. monroe17
    • 2 years ago
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    so for fof.. would is be.. (x-2)-2=x-4?

  6. jim_thompson5910
    • 2 years ago
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    no, you're not distributing since it's originally x-2 and not -2x

  7. jim_thompson5910
    • 2 years ago
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    yes, fof is x-4

  8. 85295james
    • 2 years ago
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    no the roots is X=-1 or -2

  9. monroe17
    • 2 years ago
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    what about ... (x-2)^2+3(x-2)+4?

  10. jim_thompson5910
    • 2 years ago
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    (x-2)^2+3(x-2)+4 x^2-4x+4+3(x-2)+4 x^2-4x+4+3x-6+4 x^2-x+2

  11. 85295james
    • 2 years ago
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    the polynomial discriminant: =1

  12. 85295james
    • 2 years ago
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    :)

  13. 85295james
    • 2 years ago
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    hope that helps

  14. monroe17
    • 2 years ago
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    how'd you go from (x-2)^2+3(x-2)+4 to this.. x^2-4x+4+3(x-2)+4 ?

  15. jim_thompson5910
    • 2 years ago
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    (x-2)^2 (x-2)(x-2) x(x-2) - 2(x-2) x^2 - 2x - 2x + 4 x^2 - 4x + 4

  16. jim_thompson5910
    • 2 years ago
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    So (x-2)^2 is the same as x^2 - 4x + 4

  17. jim_thompson5910
    • 2 years ago
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    which makes (x-2)^2+3(x-2)+4 the same as x^2-4x+4+3(x-2)+4

  18. monroe17
    • 2 years ago
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    yea, yeah, I wasn't thinking.

  19. jim_thompson5910
    • 2 years ago
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    that's ok

  20. monroe17
    • 2 years ago
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    lol :)

  21. monroe17
    • 2 years ago
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    I'm gonna try to do this one by myself.. and i'll report back what answer I get lol.. (x^2+3x+4)^2+3(x^2+3x+4)+4...

  22. jim_thompson5910
    • 2 years ago
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    alright

  23. monroe17
    • 2 years ago
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    is it simplified to.. x^4+3x^2+8+3x^2+9x+12+4? I know that not all the way simplified.. I just wanna know if im sorta on the right track?

  24. monroe17
    • 2 years ago
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    x^4+3x^2+16+3x^2+9x+12+4..

  25. jim_thompson5910
    • 2 years ago
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    no, you're supposed to have cubed terms in there

  26. jim_thompson5910
    • 2 years ago
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    keep in mind that (x^2+3x+4)^2 (x^2+3x+4)(x^2+3x+4) x^2(x^2+3x+4)+3x(x^2+3x+4)+4(x^2+3x+4)

  27. monroe17
    • 2 years ago
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    (x^2+3x+4)^2=x^4+6x^3+17x^2+24x+16?

  28. jim_thompson5910
    • 2 years ago
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    that is correct, so (x^2+3x+4)^2+3(x^2+3x+4)+4 becomes x^4+6x^3+17x^2+24x+16+3(x^2+3x+4)+4

  29. monroe17
    • 2 years ago
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    x^4+6x^3+20x^2+33x+24?

  30. monroe17
    • 2 years ago
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    +32*

  31. jim_thompson5910
    • 2 years ago
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    good catch

  32. jim_thompson5910
    • 2 years ago
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    x^4+6x^3+20x^2+33x+32 is the correct final answer

  33. monroe17
    • 2 years ago
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    my goodness! finally lol! Now, one final question... How do I find the domain of those... :/

  34. jim_thompson5910
    • 2 years ago
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    The domain of any polynomial is the set of all real numbers.

  35. jim_thompson5910
    • 2 years ago
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    since you can plug in any real number into a polynomial function and get a real number out.

  36. jim_thompson5910
    • 2 years ago
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    If f(x) and g(x) are both polynomial functions, then the following are also polynomial functions f(g(x)), g(f(x)), f(f(x)), and g(g(x)) or any combination of composition you can think of are all polynomial functions

  37. jim_thompson5910
    • 2 years ago
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    So the domain of each composite function is the set of all real numbers.

  38. jim_thompson5910
    • 2 years ago
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    Notice nowhere do we have to worry about a) dividing by zero or b) taking the square root of negative numbers. So there are no restrictions on x.

  39. monroe17
    • 2 years ago
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    so the domain for all four polynomials is (-inf,inf)?

  40. jim_thompson5910
    • 2 years ago
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    exactly

  41. monroe17
    • 2 years ago
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    phew.. I thought it was gonna b longer then that. lol! Thank you so much. so for any polynomial.. the domain will be (-inf,inf) because there are no restrictions?

  42. jim_thompson5910
    • 2 years ago
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    Yes, any number will do for the input of a polynomial. So the domain in interval notation for any polynomial is (-inf,inf)

  43. jim_thompson5910
    • 2 years ago
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    You'll only run into domain restrictions if you deal with division of variables or having variables in square roots (or logs)

  44. monroe17
    • 2 years ago
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    okay, I gotta remember that :) thank you!

  45. jim_thompson5910
    • 2 years ago
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    you're welcome

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