![]() In order to factor p completely one should use the field of the rationals numbers extended by the roots of the polynomial e.g. So it implies we can factorize p using an appropriate Extension. Of course, the factorization has to be done in such a manner that it keeps the differential equation operationally intact. The roots are algebraic numbers since p is a polynomial with integer coefficients : Element & s] Here F is a very long function of x,y,z as well as some other terms, A,B,C. Involving irrational numbers and therefore it cannot be factorized by default nor using Extension->I. Has three complex roots (only one real) : s = Solve = 0, x] This polynomial : p := 8 x^3 - 7 x^2 + 10 x - 5 It also multiplies, divides and finds the greatest common divisors of pairs of polynomials determines values of polynomial roots plots polynomials finds partial fraction decompositions and more. The fundamental theorem of algebra states that in principle one can always factorize any polynomial of one variable by finding its roots, nevertheless there are fundamental limitations (Galois theorem, Abel's impossibility theorem, etc.) as well as technical problems (simplifying roots in terms of nested radicals, efficency, etc.). Basic Math More than just an online factoring calculator WolframAlpha is a great tool for factoring, expanding or simplifying polynomials. any element of the extension is a finite combination of rationals and algebraics $(a_1, a_2.,a_n)$. ![]() Extension serves factorization over the rationals extended by a finite set of algebraic numbers, i.e. \) will get smaller and smaller, but the population approaches the carrying capacity as \(t\) approaches infinity.By default Mathematica can factorize polynomials to lower order ones in terms of integers if it's possible. simplifying expressions - Extract common factor from vector or matrix - Mathematica Stack Exchange Extract common factor from vector or matrix Ask Question Asked 8 years, 2 months ago Modified 1 year, 1 month ago Viewed 3k times 14 I can't believe this hasn't been asked before but I can't find anything. ![]()
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