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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=

Respuesta :

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.

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