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Math Help - Nonlinear Inequalities

  1. #1
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    Question Nonlinear Inequalities

    The problem is to solve the inequality and write the solution set in interval notation.

    (x-1)^2(x+2)^3 (greater or equal to) 0

    I get that (X-1)^2 factors out to (x-1)(x+1), but I dont know how to simplify (X+2)^3 and im not sure how to go about solving the inequality.

    HELP please asap. My chapter exam is tomorrow!!
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  2. #2
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    Quote Originally Posted by ugkwan View Post
    The problem is to solve the inequality and write the solution set in interval notation.

    (x-1)^2(x+2)^3 (greater or equal to) 0

    I get that (X-1)^2 factors out to (x-1)(x+1), but I dont know how to simplify (X+2)^3 and im not sure how to go about solving the inequality.

    HELP please asap. My chapter exam is tomorrow!!
    (x-1)^2 factors out to (x-1)(x-1). This isn't the difference between two squares. Remember that x^2-1=(x-1)(x+1), but this isn't the same as (x-1)^2=x^2-2x+1

    There is no reason to factor it anyway, it's factored enough for you already. The only zeros of this function are x=1 and x=-2.

    So now set up your test intervals to find were the function is greater than or EQUAL to zero. So you know your intervals should be closed at x=1 and x=-2. Let me know if you need more help. Lucky for you, I'll be here for a few mins.

    Test intervals:

    (-\infty,-2),(-2,1),(1,\infty)
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  3. #3
    Math Engineering Student
    Krizalid's Avatar
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    Quote Originally Posted by ugkwan View Post
    (x-1)^2(x+2)^3 (greater or equal to) 0
    Since (x-1)^2,(x+2)^2\ge0 then we only require that x\ge-2.
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