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15 February, 16:38

How do I factor x^8-80x^4-81

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  1. 15 February, 19:25
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    Which two numbers add up to - 80 and multiply to - 81?

    -81 and 1

    Rewrite the expression using the above

    (x^4 - 81) (x^4 + 1)

    Rewrite x^4 - 81 in the form; a^2 - b^2, where a = x^2 and b = 9

    ((x^2) ^2 - 9^2) (x^4 + 1)

    Use the Difference of Squares: a^2 - b^2 = (a + b) (a - b)

    (x^2 + 9) (x^2 - 9) (x^4 + 1)

    Rewrite x^2 - 9 in the form a^2 - b^2, where a = x and b = 3

    (x^2 + 9) (x^2 - 3^2) (x^4 + 1)

    Use the Difference of Squares; a^2 - b^2 = (a + b) (a - b)

    (x^2 + 9 (x + 3) (x - 3) (x^4 + 1)
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