How do you factor r^3 - 1r3−1?
1 Answer
Dec 20, 2015
Use the difference of cubes identity to find:
r^3-1 = (r-1)(r^2+r+1)r3−1=(r−1)(r2+r+1)
Explanation:
The difference of cubes identity can be written:
a^3-b^3=(a-b)(a^2+ab+b^2)a3−b3=(a−b)(a2+ab+b2)
Use this with
r^3-1r3−1
=r^3-1^3=r3−13
=(r-1)(r^2+(r)(1)+1^2)=(r−1)(r2+(r)(1)+12)
=(r-1)(r^2+r+1)=(r−1)(r2+r+1)
If you allow Complex coefficients then this can be factored a little further:
=(r-1)(r-omega)(r-omega^2)=(r−1)(r−ω)(r−ω2)
where
