Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

When (x^9 - x) is factored as completely as possible into polynomials and monomials with integral coefficients, how many factors are there?

When X9 X Is Factored As Completely As Possible Into Polynomials And Monomials With Integral Coefficients How Many Factors Are There class=

Sagot :

Notice that

[tex](x^9-x)=x(x^8-1)[/tex]

Furthermore,

[tex](x^8-1)=(x^4+1)(x^4-1)=(x^4+1)(x^2+1)(x^2-1)=(x^4+1)(x^2+1)(x+1)(x-1)[/tex]

Then,

[tex](x^9-x)=x(x^4+1)(x^2+1)(x+1)(x-1)[/tex]

This expression cannot be further simplified. There are 5 factors in total, one monomial and four binomials.