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Factorization of a binomial

Source:

March 3, 2010
algebrapolynomialcalculusintegration

Problem Statement

When x^9\minus{}x is factored as completely as possible into polynomials and monomials with integral coefficients, the number of factors is: <spanclass=latexbold>(A)</span> more than 5<spanclass=latexbold>(B)</span> 5<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 2 <span class='latex-bold'>(A)</span>\ \text{more than 5} \qquad <span class='latex-bold'>(B)</span>\ 5 \qquad <span class='latex-bold'>(C)</span>\ 4 \qquad <span class='latex-bold'>(D)</span>\ 3 \qquad <span class='latex-bold'>(E)</span>\ 2