Question

若关于xy的多项式：x的m-2次方乘y的平方+mx的m-2次方乘y+nx的立方乘y的m-3次方-2

Answer 1

x^(m-2) * y^2 + mx^(m-2) * y + nx^3 * y^(m-3) - 2x^(m^2 -6m+9) +m+n化简后是四次三项式,x^(m-2) * y^2 或nx^3 * y^(m-3)或2x^(m^2 -6m+9)是四次式,m-2或m-3或m^2 -6m+9=4 ,根据运算,当m^2 -6m+9=4 是才满足x^(m-2) * y^2 + mx^(m-2) * y + nx^3 * y^(m-3) - 2x^(m^2 -6m+9) +m+n化简后是四次式,m=5,x^(m-2) * y^2 + mx^(m-2) * y + nx^3 * y^(m-3) - 2x^(m^2 -6m+9) +m+n化简后是三项式,把m=-5带入得x^3* y^2 + 5x^ * y + nx^3 * y^2 - 2x^4 +5+n,因为是三项式x^3* y^2+ nx^3 * y^2=0x^3 * y^2即1+n=0,n= -1