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7 June, 02:21

Determine the linear factors for x4-2x^2+1

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Answers (2)
  1. 7 June, 02:29
    0
    Didn't you mean x^4-2x^2+1?

    Choose "p" to represent x^2. Then p^2 - 2p + 1 = (p-1) (p-1)

    These results are equivalent to (x^2-1) (x^2+1).

    x^2-1 can be factored: (x-1) (x+1)

    x^2-1 (again) can be factored: (x-1) (x+1)

    Then the factored expression is (x-1) ^2 * (x+1) ^2.

    Check this by multiplication. Do you obtain x^4 - 2x^2 + 1?
  2. 7 June, 02:30
    0
    Use a substitution: let b = x^2

    Then b^2 = x^4.

    Now you need to factor

    b^2 - 2b + 1 =

    (b - 1) ^2

    Since b = x^2, now we replace b with x^2 and factor again.

    (x^2 - 1) ^2 is the square of a difference of squares.

    = (x^2 - 1) (x^2 - 1)

    = (x + 1) (x - 1) (x + 1) (x - 1)

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