Home/Algebra/Polynomials/Multivariable polynomial11. PolynomialsMultivariable polynomialLevel: intermedioIn 11. PolynomialsFormulaCopy LaTeXP(x1,…,xn)=∑αcαx1α1⋯xnαn,P(x_1,\ldots,x_n) = \sum_{\boldsymbol\alpha}c_{\boldsymbol\alpha} x_1^{\alpha_1}\cdots x_n^{\alpha_n},P(x1,…,xn)=α∑cαx1α1⋯xnαn,Tagsalgebraalgebra formulapolynomialsDetailGeneralizes single-variable polynomials to expressions in several algebraic variables.Explore the ideaFound an error? Contact us.Related formulasRelatedPolynomial of degree nP(x)=anxn+an−1xn−1+⋯+a1x+a0P(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0P(x)=anxn+an−1xn−1+⋯+a1x+a0Open formulaOpen in sectionRelatedMulti-index and total degreex1α1⋯xnαn,x_1^{\alpha_1}\cdots x_n^{\alpha_n},x1α1⋯xnαn,Open formulaOpen in sectionRelatedHomogeneous polynomialP(x,y)=x2+3xy+2y2P(x,y)=x^2+3xy+2y^2P(x,y)=x2+3xy+2y2Open formulaOpen in sectionRelatedSystem of polynomial equations{P1(x1,…,xn)=0⋮Pm(x1,…,xn)=0.\begin{cases} P_1(x_1,\ldots,x_n)=0\\ \vdots\\ P_m(x_1,\ldots,x_n)=0. \end{cases}⎩⎨⎧P1(x1,…,xn)=0⋮Pm(x1,…,xn)=0.Open formulaOpen in section