Question

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)

Answer 1

Option a.

Explanation:

The given expression is

`x^6+2x^3+1`

Splitting the middle term, it can be rewritten as

`x^6+x^3+x^3+1`

`(x^6+x^3)+(x^3+1)`

Taking out GCF fro each parenthesis.

`x^3(x^3+1)+1(x^3+1)`

`(x^3+1)(x^3+1)`

`(x^3+1)^2`

Therefore, the correct option is a.