Exercise
$1-x^8$
Step-by-step Solution
Learn how to solve common monomial factor problems step by step online. Factor the expression 1-x^8. For easier handling, reorder the terms of the polynomial -x^8+1 from highest to lowest degree. We can factor the polynomial -x^8+1 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 1. Next, list all divisors of the leading coefficient a_n, which equals 1. The possible roots \pm\frac{p}{q} of the polynomial -x^8+1 will then be.
Factor the expression 1-x^8
Final answer to the exercise
$-\left(x^{7}+x^{6}+x^{5}+x^{4}+x^{3}+x^2+x+1\right)\left(x-1\right)$