How do you factor x^6+2x^3+1 ?

1 Answer
Jul 1, 2015

x^6+2x^3+1 = (x+1)^2(x^2-x+1)^2

Explanation:

x^6+2x^3+1

=(x^3)^2+2(x^3)+1

=(x^3+1)^2

=(x^3+1^3)^2

=(x+1)^2(x^2-x+1)^2

Using the sum of cubes identity:

a^3+b^3 = (a+b)(a^2-ab+b^2)

with a=x and b=1

(x^2-x+1) has no simpler factors with real coefficients.