整式降幂典型题目及答案

整式降幂典型题目及答案

一、单项选择题1.把多项式\(3x^2+5-2x^3-4x\)按\(x\)的降幂排列后，第三项是（）A.\(3x^2\)B.\(-2x^3\)C.\(-4x\)D.\(5\)答案：C2.多项式\(4x^3-3x^2y^4+2x-7\)的各项按照\(y\)的降幂排列为（）A.\(-3x^2y^4+4x^3+2x-7\)B.\(4x^3-3x^2y^4+2x-7\)C.\(-7+2x+4x^3-3x^2y^4\)D.\(-3x^2y^4-7+2x+4x^3\)答案：A3.多项式\(x^4-3x^3y+3x^2y^2-xy^3+y^4\)按\(x\)降幂排列正确的是（）A.\(x^4-3x^3y-xy^3+3x^2y^2+y^4\)B.\(x^4-3x^3y+3x^2y^2-xy^3+y^4\)C.\(y^4-xy^3+3x^2y^2-3x^3y+x^4\)D.\(-3x^3y+3x^2y^2-xy^3+y^4+x^4\)答案：B4.将多项式\(2x^2y-4y^3+5xy^2-x^3\)按\(x\)的降幂排列为（）A.\(-x^3+2x^2y+5xy^2-4y^3\)B.\(2x^2y-x^3+5xy^2-4y^3\)C.\(-4y^3+5xy^2+2x^2y-x^3\)D.\(-x^3-4y^3+2x^2y+5xy^2\)答案：A5.多项式\(3x^2y-2xy^2+\frac{1}{2}x^3-\frac{1}{3}y^3\)按\(y\)的降幂排列是（）A.\(-\frac{1}{3}y^3-2xy^2+3x^2y+\frac{1}{2}x^3\)B.\(\frac{1}{2}x^3+3x^2y-2xy^2-\frac{1}{3}y^3\)C.\(-\frac{1}{3}y^3-2xy^2+\frac{1}{2}x^3+3x^2y\)D.\(\frac{1}{2}x^3-2xy^2+3x^2y-\frac{1}{3}y^3\)答案：A6.把多项式\(2x^3-5x^2-3x+4\)按\(x\)的降幂排列，正确的是（）A.\(2x^3-5x^2-3x+4\)B.\(4-3x-5x^2+2x^3\)C.\(-5x^2+2x^3-3x+4\)D.\(2x^3+5x^2-3x+4\)答案：A7.多项式\(a^3-2a^2b+3ab^2-b^3\)按\(a\)的降幂排列是（）A.\(a^3-2a^2b+3ab^2-b^3\)B.\(-b^3+3ab^2-2a^2b+a^3\)C.\(a^3-b^3-2a^2b+3ab^2\)D.\(3ab^2-2a^2b+a^3-b^3\)答案：A8.把多项式\(4a^3b-3ab^2+a^4-5b^5\)按\(b\)的降幂排列是（）A.\(-5b^5-3ab^2+4a^3b+a^4\)B.\(a^4+4a^3b-3ab^2-5b^5\)C.\(-5b^5+4a^3b-3ab^2+a^4\)D.\(-5b^5-3ab^2+a^4+4a^3b\)答案：A9.多项式\(x^3-2x^2y^2+3y^3\)按\(x\)降幂排列为（）A.\(x^3-2x^2y^2+3y^3\)B.\(3y^3-2x^2y^2+x^3\)C.\(x^3+3y^3-2x^2y^2\)D.\(-2x^2y^2+x^3+3y^3\)答案：A10.多项式\(5x^2y-3xy^2+4x^3-y^3\)按\(y\)的降幂排列是（）A.\(-y^3-3xy^2+5x^2y+4x^3\)B.\(4x^3+5x^2y-3xy^2-y^3\)C.\(-y^3+4x^3-3xy^2+5x^2y\)D.\(-y^3-3xy^2+4x^3+5x^2y\)答案：A二、多项选择题1.下列关于多项式按某一字母降幂排列正确的有（）A.多项式\(2x^2-3x+5x^3-1\)按\(x\)降幂排列为\(5x^3+2x^2-3x-1\)B.多项式\(a^2b-ab^2+a^3-b^3\)按\(a\)降幂排列为\(a^3+a^2b-ab^2-b^3\)C.多项式\(3x^2y-2xy^2+y^3-x^3\)按\(y\)降幂排列为\(y^3-2xy^2+3x^2y-x^3\)D.多项式\(m^3-2m^2n+3mn^2-n^3\)按\(m\)降幂排列为\(m^3-2m^2n+3mn^2-n^3\)答案：ABCD2.以下多项式按要求降幂排列正确的是（）A.多项式\(4x^3-5x^2+2x-1\)按\(x\)降幂排列为\(4x^3-5x^2+2x-1\)B.多项式\(a^2b-3ab^2+2a^3-b^3\)按\(a\)降幂排列为\(2a^3+a^2b-3ab^2-b^3\)C.多项式\(2x^2y-4xy^2+3y^3-x^3\)按\(y\)降幂排列为\(3y^3-4xy^2+2x^2y-x^3\)D.多项式\(p^3-2p^2q+3pq^2-q^3\)按\(p\)降幂排列为\(p^3-2p^2q+3pq^2-q^3\)答案：ABCD3.对于多项式降幂排列，下列说法正确的是（）A.多项式\(3x^2-2x^3+5x-1\)按\(x\)降幂排列为\(-2x^3+3x^2+5x-1\)B.多项式\(ab^2-a^2b+a^3-b^3\)按\(a\)降幂排列为\(a^3-a^2b+ab^2-b^3\)C.多项式\(4x^2y-3xy^2+y^3-x^3\)按\(y\)降幂排列为\(y^3-3xy^2+4x^2y-x^3\)D.多项式\(m^3-3m^2n+2mn^2-n^3\)按\(m\)降幂排列为\(m^3-3m^2n+2mn^2-n^3\)答案：ABCD4.下列多项式按指定字母降幂排列正确的有（）A.多项式\(5x^2-4x^3+3x-2\)按\(x\)降幂排列为\(-4x^3+5x^2+3x-2\)B.多项式\(a^2b-4ab^2+3a^3-b^3\)按\(a\)降幂排列为\(3a^3+a^2b-4ab^2-b^3\)C.多项式\(3x^2y-5xy^2+4y^3-x^3\)按\(y\)降幂排列为\(4y^3-5xy^2+3x^2y-x^3\)D.多项式\(p^3-4p^2q+3pq^2-q^3\)按\(p\)降幂排列为\(p^3-4p^2q+3pq^2-q^3\)答案：ABCD5.以下关于多项式降幂排列正确的是（）A.多项式\(6x^2-7x^3+4x-1\)按\(x\)降幂排列为\(-7x^3+6x^2+4x-1\)B.多项式\(a^2b-5ab^2+4a^3-b^3\)按\(a\)降幂排列为\(4a^3+a^2b-5ab^2-b^3\)C.多项式\(5x^2y-6xy^2+5y^3-x^3\)按\(y\)降幂排列为\(5y^3-6xy^2+5x^2y-x^3\)D.多项式\(m^3-5m^2n+4mn^2-n^3\)按\(m\)降幂排列为\(m^3-5m^2n+4mn^2-n^3\)答案：ABCD6.下列多项式按字母降幂排列正确的是（）A.多项式\(7x^2-8x^3+5x-2\)按\(x\)降幂排列为\(-8x^3+7x^2+5x-2\)B.多项式\(a^2b-6ab^2+5a^3-b^3\)按\(a\)降幂排列为\(5a^3+a^2b-6ab^2-b^3\)C.多项式\(6x^2y-7xy^2+6y^3-x^3\)按\(y\)降幂排列为\(6y^3-7xy^2+6x^2y-x^3\)D.多项式\(p^3-6p^2q+5pq^2-q^3\)按\(p\)降幂排列为\(p^3-6p^2q+5pq^2-q^3\)答案：ABCD7.对于多项式降幂排列的相关内容，以下正确的是（）A.多项式\(8x^2-9x^3+6x-3\)按\(x\)降幂排列为\(-9x^3+8x^2+6x-3\)B.多项式\(a^2b-7ab^2+6a^3-b^3\)按\(a\)降幂排列为\(6a^3+a^2b-7ab^2-b^3\)C.多项式\(7x^2y-8xy^2+7y^3-x^3\)按\(y\)降幂排列为\(7y^3-8xy^2+7x^2y-x^3\)D.多项式\(m^3-7m^2n+6mn^2-n^3\)按\(m\)降幂排列为\(m^3-7m^2n+6mn^2-n^3\)答案：ABCD8.下列关于多项式按字母降幂排列正确的有（）A.多项式\(9x^2-10x^3+7x-4\)按\(x\)降幂排列为\(-10x^3+9x^2+7x-4\)B.多项式\(a^2b-8ab^2+7a^3-b^3\)按\(a\)降幂排列为\(7a^3+a^2b-8ab^2-b^3\)C.多项式\(8x^2y-9xy^2+8y^3-x^3\)按\(y\)降幂排列为\(8y^3-9xy^2+8x^2y-x^3\)D.多项式\(p^3-8p^2q+7pq^2-q^3\)按\(p\)降幂排列为\(p^3-8p^2q+7pq^2-q^3\)答案：ABCD9.以下多项式降幂排列正确的是（）A.多项式\(10x^2-11x^3+8x-5\)按\(x\)降幂排列为\(-11x^3+10x^2+8x-5\)B.多项式\(a^2b-9ab^2+8a^3-b^3\)按\(a\)降幂排列为\(8a^3+a^2b-9ab^2-b^3\)C.多项式\(9x^2y-10xy^2