How do you factor #x^3+343#?
1 Answer
Apr 23, 2016
#x^3+343=(x+7)(x^2-7x+49)#
Explanation:
The sum of cubes identity can be written:
#a^3+b^3 = (a+b)(a^2-ab+b^2)#
We can use this with
#x^3+343#
#=x^3+7^3#
#=(x+7)(x^2-7x+7^2)#
#=(x+7)(x^2-7x+49)#
The remaining quadratic factor can only be factored further with Complex coefficients, which we can express in terms of the primitive Complex cube root of
#=(x+7)(x+7omega)(x+7omega^2)#
where
