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5.1 Mathematical Manipulations • 153> Factor( x^3+1 ) mod 5;(x 2 + 4 x + 1) (x + 1)> Factor( x^3+1, RootOf(x^2+x+1) ) mod 5;(x + 4 RootOf(_Z 2 + _Z + 1) + 4) (x + 1)(x + RootOf(_Z 2 + _Z + 1))For details about the algorithm used, factoring multivariate polynomials,or factoring polynomials over an algebraic number field, refer to?Factor.Removing Rational ExponentsIn general, it is preferred to represent rational expressions without fractionalexponents in the denominator. The rationalize command removesroots from the denominator of a rational expression by multiplyingby a suitable factor.> 1 / ( 2 + root[3](2) );12 + 2 ( 1 3 )> rationalize( % );25 − 1 5 2( 1 3 ) + 110 2( 2 3 )> (x^2+5) / (x + x^(5/7));x 2 + 5x + x ( 5 7 )> rationalize( % );(x 2 + 5) (x ( 6 7 ) − x ( 12 7 ) − x ( 4 7 ) + x ( 107 ) + x ( 2 7 ) − x ( 8 7 ) + x 2 )/(x 3 + x)The result of rationalize is often larger than the original.