Posted by Donielle on .
Look at the following polynomials and their factorizations:
x^21=(x1)(x+1)
x^31=(x1)(x^2+x+1)
x^41=(x1)(x^3+x^2+x+1)
In general, how can x^n1 be factored. Show that this factorization works by multiplying the factors

Algebra 2 
Steve,
Just do a long multiplication and line up the like exponents:
You'll notice that all the exponents have a plus entry and a minus entry, except the highest and lowest:
x^n + x^n1 + x^n2 + ... + x^2 + x^1
000  x^n1  x^n2  ...  x^2  x^1  1

x^n  1