Please show me how to factor X⁴ – 1 = Please show the steps. thank you very much, Jim

Question

Please show me how to factor X⁴ – 1 =

Please show the steps. thank you very much, Jim

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Thu Hương 4 years 2021-08-02T16:02:38+00:00 1 Answers 18 views 0

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  1. taiduc
    0
    2021-08-02T16:04:01+00:00
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    Answer:

    factoring the term x^4-1 we get \mathbf{(x^2+1)(x-1)(x+1}

    Step-by-step explanation:

    We need to factor the term x^4-1

    We know that a^2-b^2=(a-b)(a+b)

    We can write x^4 \ as \ (x^2)^2

    Simplifying:

    x^4-1\\=(x^2)^2-1\\=(x^2-1)(x^2+1)\\

    Now, again using formula a^2-b^2=(a-b)(a+b)

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

    So, factoring the term x^4-1 we get \mathbf{(x^2+1)(x-1)(x+1}

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