多項(xiàng)式乘除典型題目及答案一、選擇題（共20分）1.多項(xiàng)式\((x^2+3x+2)\)與\((x-1)\)的乘積是（）。（5分）A.\(x^3-1\)B.\(x^3+2x^2+x-2\)C.\(x^3-x^2+2x-2\)D.\(x^3+x^2-2x-2\)2.多項(xiàng)式\((2x^2-3x+1)\)除以\((x-1)\)的商是（）。（5分）A.\(2x+1\)B.\(2x+3\)C.\(2x-1\)D.\(2x-3\)3.多項(xiàng)式\((x^3-2x^2+3x-4)\)除以\((x-2)\)的余數(shù)是（）。（5分）A.0B.2C.4D.84.多項(xiàng)式\((x^4+2x^3-x^2-2x+1)\)除以\((x^2+x-2)\)的商是（）。（5分）A.\(x^2+x+1\)B.\(x^2-x+1\)C.\(x^2+3x+1\)D.\(x^2-3x+1\)二、填空題（共20分）1.計(jì)算多項(xiàng)式\((x^2+4x+3)\)與\((x-2)\)的乘積，結(jié)果為：\(\_\_\_\_\_\_\_\_\_\_\)。（5分）2.計(jì)算多項(xiàng)式\((3x^3-2x^2+x-5)\)除以\((x+1)\)的商，結(jié)果為：\(\_\_\_\_\_\_\_\_\_\_\)。（5分）3.計(jì)算多項(xiàng)式\((x^4-3x^3+2x^2+5x-6)\)除以\((x-2)\)的余數(shù)，結(jié)果為：\(\_\_\_\_\_\_\_\_\_\_\)。（5分）4.計(jì)算多項(xiàng)式\((2x^3+5x^2-3x-7)\)除以\((x^2-1)\)的商，結(jié)果為：\(\_\_\_\_\_\_\_\_\_\_\)。（5分）三、解答題（共60分）1.計(jì)算多項(xiàng)式\((x^3+2x^2-3x+4)\)與\((x+1)\)的乘積，并寫(xiě)出完整的計(jì)算過(guò)程。（15分）2.計(jì)算多項(xiàng)式\((4x^4-3x^3+2x^2-x+5)\)除以\((x-1)\)的商和余數(shù)，并寫(xiě)出完整的計(jì)算過(guò)程。（15分）3.計(jì)算多項(xiàng)式\((x^5-2x^4+3x^3-4x^2+5x-6)\)除以\((x^2+2x+1)\)的商，并寫(xiě)出完整的計(jì)算過(guò)程。（15分）4.計(jì)算多項(xiàng)式\((3x^4+2x^3-5x^2+7x-11)\)除以\((x^2-3x+2)\)的商和余數(shù)，并寫(xiě)出完整的計(jì)算過(guò)程。（15分）答案一、選擇題1.正確答案：D.\(x^3+x^2-2x-2\)2.正確答案：B.\(2x+3\)3.正確答案：D.84.正確答案：A.\(x^2+x+1\)二、填空題1.\(x^3+2x^2-5x-6\)2.\(3x^2-5x+4\)3.44.\(2x+7\)三、解答題1.計(jì)算過(guò)程：\[(x^3+2x^2-3x+4)(x+1)=x^4+x^3+2x^3+2x^2-3x^2-3x+4x+4=x^4+3x^3-x^2+x+4\]2.計(jì)算過(guò)程：\[\begin{align}\text{商}&=4x^3-x^2-2x+5\\\text{余數(shù)}&=-2\end{align}\]驗(yàn)證：\(4x^4-3x^3+2x^2-x+5=(x-1)(4x^3-x^2-2x+5)-2\)3.計(jì)算過(guò)程：\[\begin{align}\text{商}&=x^3-4x^2+5x-6\end{align}\]驗(yàn)證：\(x^5-2x^4+3x^3-4x^2+5x-6=(x^2+2x+1)(x^3-4x^2+5x-6)\)4.計(jì)算過(guò)程：\[\begin{align}\text{商}&=3x^2+7x-11\\\text{