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elena-14-01-66 [18.8K]
3 years ago
15

Which of these represents the factorization of x4−256 ?

Mathematics
1 answer:
Goshia [24]3 years ago
5 0

Answer:

(x+4)(x-4)(x+4i)(x-4i) (answer D)

Step-by-step explanation:

We can re-write the original binomial as a difference of squares noticing that 456=16^2 and that x^4=(x^2)^2

Then we have:

x^4-256=(x^2)^2-16^2

Then we can factor this out using the difference of squares factor form:

(x^2)^2-16^2=(x^2+16)(x^2-16)

Now, (x^2-16), is itself a difference of squares which we can factor out further:x^2-16=x^2-4^2=(x+4)(x-4)

And we can also solve for the binomial: (x^2+16):

x^2+16=0\\x^2=-16\\x=+/-\sqrt{-16} \\x=+/-i\,\sqrt{16} \\x=+/-4\,i

then we can write (x^2+16)=(x+4i)(x-4i)

Therefore, the final factor form of the original binomial is the product of all factors we found: (x+4)(x-4)(x+4i)(x-4i)

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