contestada

Which expression correctly shows x6+2x3+1 factored completely over the integers?

a) (x3+1)2
b) (x+1)2(x2−x+1)2
c) (x+1)(x2−x+1)
d) (x2+1)(x4−x2+1)

Respuesta :

Answer:

Option a.

Step-by-step explanation:

The given expression is

[tex]x^6+2x^3+1[/tex]

Splitting the middle term, it can be rewritten as

[tex]x^6+x^3+x^3+1[/tex]

[tex](x^6+x^3)+(x^3+1)[/tex]

Taking out GCF fro each parenthesis.

[tex]x^3(x^3+1)+1(x^3+1)[/tex]

[tex](x^3+1)(x^3+1)[/tex]

[tex](x^3+1)^2[/tex]

Therefore, the correct option is a.

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