Question

18．已知多項(xiàng)式-2x²y^m+1+xy²-3x³-6是六次四項(xiàng)式，單項(xiàng)式3x²ⁿy^5-m與該多項(xiàng)式次數(shù)相同，則mn=6．

Answer 1

分析 利用多項(xiàng)式的次數(shù)定義得出m的值，進(jìn)而利用單項(xiàng)式的次數(shù)得出n的值，即可得出答案．

解答 解：∵多項(xiàng)式-2x²y^m+1+xy²-3x³-6是六次四項(xiàng)式，單項(xiàng)式3x²ⁿy^5-m與該多項(xiàng)式次數(shù)相同，
∴$\left\{\begin{array}{l}{2+m+1=6}\\{2n+5-m=6}\end{array}\right.$，
解得$\left\{\begin{array}{l}{m=3}\\{n=2}\end{array}\right.$，
則mn=3×2=6．
故答案是：6．

點(diǎn)評 此題主要考查了多項(xiàng)式與單項(xiàng)式，正確把握多項(xiàng)式次數(shù)的定義是解題關(guān)鍵．