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Math Help - PLEASE HELP! 2 quick questions! thanks!

  1. #1
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    Wink PLEASE HELP! 2 quick questions! thanks!

    I need help getting the answers for these 2 questions!
    I want to see if i did them right... (because i dont have an answer sheet)



    1) Solve 12x^3 - 16x^2 + 7x -1
    Let f(x) = 12x^3 - 16x^2 + 7x -1


    2) Solve the inequality:
    3x / (x^2 -4) < -1

    *note: where the "<" is, its supposed to be less than/equal to. (i just cant find a key for it :P )

    Thanks again!
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  2. #2
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    Quote Originally Posted by xo-hikari View Post
    I need help getting the answers for these 2 questions!
    I want to see if i did them right... (because i dont have an answer sheet)



    1) Solve 12x^3 - 16x^2 + 7x -1
    Let f(x) = 12x^3 - 16x^2 + 7x -1


    2) Solve the inequality:
    3x / (x^2 -4) < -1

    *note: where the "<" is, its supposed to be less than/equal to. (i just cant find a key for it :P )

    Thanks again!
    1) 12x^3 - 16x^2 + 7x - 1 = 12x^3 - 12x^2 - 4x^2 + 3x + 4x - 1 = (12 x^3 - 12x^2 + 3x) - (4x^2 - 4x + 1)  = 3x(4x^2 - 4x + 1) - (4x^2 - 4x + 1) = \, ....

    2) Case 1: Solve 3x \leq -(x^2 - 4) for x^2 - 4 > 0 \Rightarrow x > 2 \, \text{or} \, x < -2.

    Case 2: Solve 3x \geq -(x^2 - 4) for x^2 - 4 \leq 0 \Rightarrow -2 \leq x \leq 2.
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