Home/Algebra/Polynomials/Factorization by roots11. PolynomialsFactorization by rootsLevel: intermedioIn 11. PolynomialsFormulaCopy LaTeXP(x)=an∏k=1n(x−rk)P(x)=a_n\prod_{k=1}^{n}(x-r_k)P(x)=ank=1∏n(x−rk)Tagsalgebraalgebra formulapolynomialsDetailComplete factorization over a field that contains the roots.Found an error? Contact us.Related formulasRelatedFactor theoremP(a)=0 ⟺ (x−a) es factor de P(x)P(a)=0\iff(x-a)\text{ es factor de }P(x)P(a)=0⟺(x−a) es factor de P(x)Open formulaOpen in sectionRelatednth rootswk=r1/nei(θ+2πk)/nw_k=r^{1/n}e^{i(\theta+2\pi k)/n}wk=r1/nei(θ+2πk)/nOpen formulaOpen in section