How do you factor completely 1+x3?
1 Answer
Dec 20, 2015
Use the sum of cubes identity to find:
1+x3=(1+x)(1−x+x2)
Explanation:
The sum of cubes identity may be written:
a3+b3=(a+b)(a2−ab+b2)
In our example, we have
1+x3
=13+x3
=(1+x)(12−(1)(x)+x2)
=(1+x)(1−x+x2)
The remaining quadratic factor
=(1+x)(1+ωx)(1+ω2x)
or if you prefer:
=(1+x)(ω+x)(ω2+x)
where