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Math Help - Pre-Calc Questions including division, critical numbers, and Inequalities

  1. #1
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    Pre-Calc Questions including division, critical numbers, and Inequalities

    Any help is greatly appreciated.

    Thanks!

    1. Solve the inequality and graph the solution on the real number line.
    x3 + 3x2 9x 27 ≤ 0

    2. Find the critical numbers of the expression. (Enter your answers as a comma-separated list.)
    3x3 32x2

    3. Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero f(x) = x3 + x2 + 4x + 4 2i

    4. Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 4, 4i, 4i

    5. Use long division to divide. (8x3 + 4x2 + 2x + 5) (2x2 + 1)
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  2. #2
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    Quote Originally Posted by 305boy View Post
    Any help is greatly appreciated.

    Thanks!

    1. Solve the inequality and graph the solution on the real number line.
    x3 + 3x2 9x 27 ≤ 0

    start by factoring the left side of the inequality using the grouping method

    2. Find the critical numbers of the expression. (Enter your answers as a comma-separated list.)
    3x3 32x2

    set the expression equal to 0 and solve for x

    3. Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero f(x) = x3 + x2 + 4x + 4 2i

    if 2i is a root, then so is -2i ... the last root will be real. also note that f(x) will factor.

    4. Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 4, 4i, 4i

    \textcolor{blue}{f(x) = (x-r_1)(x-r_2)(x-r_3)} where each "r" is a zero

    5. Use long division to divide. (8x3 + 4x2 + 2x + 5) (2x2 + 1)

    it's kind of difficult to show long division in this venue

    note this link ...


    Polynomial Long Division
    in future, note that exponents can be designated by the caret symbol, i.e. x "squared" can be written x^2
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  3. #3
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    Quote Originally Posted by 305boy View Post
    Any help is greatly appreciated.

    Thanks!

    1. Solve the inequality and graph the solution on the real number line.
    x3 + 3x2 9x 27 ≤ 0

    2. Find the critical numbers of the expression. (Enter your answers as a comma-separated list.)
    3x3 32x2

    3. Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero f(x) = x3 + x2 + 4x + 4 2i

    4. Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 4, 4i, 4i

    5. Use long division to divide. (8x3 + 4x2 + 2x + 5) (2x2 + 1)
    What is the significance of the red numbers? In any case, what have you tried and what has you stumped?
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  4. #4
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    The red are the "important numbers".

    I'm assuming he is copying and pasting from an online homework website such as WebAssign or something similar. :P
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