How do you factor # x^3 - 1#?
2 Answers
Expanding upon prior answer:
Explanation:
I want to expand upon an idea expressed in the prior answer
The idea of:
or not in sigma notation:
We can prove this via induction:
Basis case :
Hence basis case holds
Induction:
Assume
Hence this is also what we yield when plugging directly into formula:
Hence holds for all
I thought this was a nice idea to consider!
Explanation:
#x^3-1" is a "color(blue)"difference of cubes"#
#•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)#
#"here "a=x" and "b=1#
#rArrx^3-1=(x-1)(x^2+x+1)#