How do you factor #x^6+10x^3+25#?
1 Answer
Sep 2, 2016
Explanation:
The sum of cubes identity can be written:
#a^3+b^3=(a+b)(a^2-ab+b^2)#
Use this with
#x^6+10x^3+25 = (x^3)^2+2(5)(x^3)+(5)^2#
#color(white)(x^6+10x^3+25) = (x^3+5)^2#
#color(white)(x^6+10x^3+25) = (x^3+(root(3)(5))^3)^2#
#color(white)(x^6+10x^3+25) = ((x+root(3)(5))(x^2-x(root(3)(5))+(root(3)(5))^2))^2#
#color(white)(x^6+10x^3+25) = (x+root(3)(5))^2(x^2-(root(3)(5))x+root(3)(25))^2#