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

Answer:

Option a.

Step-by-step 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.