Factor the polynomial completely. x^4 – 256

Question

Factor the polynomial completely.
x^4 – 256

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King 3 years 2021-07-18T18:12:44+00:00 1 Answers 8 views 0

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  1. huyenthanh
    0
    2021-07-18T18:14:21+00:00
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    Answer:

    (x²+16)(X+4)(x-4)

    Step-by-step explanation:

    x⁴ can be written as (x²)²

    256 can be written as (16)²

    by identity. a²-b²= (a+b)(a-b) :

    (x²+16)(x²-16)

    x²-16 can be written as (x)²- 4²

    by identity. a²-b²= (a+b)(a-b) :

    (X+4)(x-4)

    Therefore, the factors altogether would be

    (x²+16)(x+4)(x-4)

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