Factor Theorem: Solving a^5-32

[Rowah]

Simple Factoring Problem

How do I factor $$a^5-32$$?

It isn't a difference of cubes or even a difference of squares :(

By the way, we're currently learning the factor theorem.

 

[semc]

let f(a)= $$a^5-32$$ .when x=2,f(a)=0 so a-2 is a factor of the funtion. suppose you know how to carry on since you learned factor theorem?

 

[radou]

Use the rule $$a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^2+\cdots+ab^{n-2}+b^{n-1}), n \in \textbf{N}$$.

 

[Rowah]

Cool, I understand now, thanks, "a" messed me up, I didn't know you could do f(a), I thought it was only f(x).