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How do you factor #x^3+1?

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May 6, 2015

#x^3+1 = x^3 + 1^3#

The sum of cubes identity tells us that :

#color(blue)(a^3 + b^3 = (a + b)(a^2 - ab + b^2)#

Hence # x^3 + 1^3 = (x + 1)(x^2 - (x*1) + 1^2)#

# = color(green)((x + 1)(x^2 - x + 1)#

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