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2 March, 12:32

What is the completely factored form of x^4+8x^2-9

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Answers (2)
  1. 2 March, 12:37
    0
    Remark

    You'll see it a whole lot easier if you make a substitution so that it looks like something you have already seen

    Solution

    let y = x^2

    x^4 = x^2 * x^2

    x^4 = y * y

    x^4 = y^2

    Now the expression becomes

    y^2 + 8 y - 9 = z

    (y + 9) (y - 1) = z

    Now put the x^2 back in.

    (x^2 + 9) (x^2 - 1) = z

    x^2 - 1 becomes x + 1 and x - 1. At this level x^2 + 9 can't be factored.

    Answer

    (x^2 + 9) (x + 1) (x - 1)
  2. 2 March, 12:39
    0
    Answer: (x+1) (x-1) (x^2+9)
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