整式次數(shù)系數(shù)題目及答案

整式次數(shù)系數(shù)題目及答案一、選擇題1.已知多項(xiàng)式\(P(x)=3x^3-5x^2+7x-9\)，下列關(guān)于該多項(xiàng)式的描述中，正確的是：A.這是一個(gè)一次多項(xiàng)式B.這是一個(gè)二次多項(xiàng)式C.這是一個(gè)三次多項(xiàng)式D.這是一個(gè)四次多項(xiàng)式答案：C2.對(duì)于多項(xiàng)式\(Q(x)=2x^4-3x^3+5x^2-7\)，下列說(shuō)法正確的是：A.該多項(xiàng)式的次數(shù)是4B.該多項(xiàng)式的次數(shù)是3C.該多項(xiàng)式的次數(shù)是2D.該多項(xiàng)式的次數(shù)是1答案：A3.若多項(xiàng)式\(R(x)=ax^2+bx+c\)的系數(shù)\(a=0\)，則該多項(xiàng)式的次數(shù)為：A.2B.1C.0D.不能確定答案：B4.多項(xiàng)式\(S(x)=4x^3-2x^2+5\)的最高次項(xiàng)系數(shù)是：A.4B.-2C.5D.0答案：A5.多項(xiàng)式\(T(x)=-x^5+3x^4-2x^3+7x^2-5x+1\)的常數(shù)項(xiàng)是：A.-1B.1C.5D.7答案：B二、填空題6.多項(xiàng)式\(U(x)=6x^5-4x^4+2x^3-8x^2+x-3\)的次數(shù)是________。答案：57.多項(xiàng)式\(V(x)=7x^3-2x^2+9x-11\)的常數(shù)項(xiàng)是________。答案：-118.若多項(xiàng)式\(W(x)=5x^n+3x^{n-1}-2x^2+x-7\)的次數(shù)是4，則\(n\)的值是________。答案：49.多項(xiàng)式\(X(x)=ax^3+bx^2+cx+d\)的次數(shù)是3，且\(a\neq0\)，則\(a\)是該多項(xiàng)式的________。答案：最高次項(xiàng)系數(shù)10.多項(xiàng)式\(Y(x)=2x^4+0x^3-5x^2+7x-9\)的最高次項(xiàng)系數(shù)是________。答案：2三、解答題11.已知多項(xiàng)式\(Z(x)=3x^4-6x^3+12x^2-24x+48\)，請(qǐng)找出該多項(xiàng)式的系數(shù)和次數(shù)。答案：該多項(xiàng)式的系數(shù)分別是3，-6，12，-24，48。該多項(xiàng)式的次數(shù)是4。12.給定多項(xiàng)式\(A(x)=-2x^5+4x^4-6x^3+8x^2-10x+12\)，求出該多項(xiàng)式的常數(shù)項(xiàng)和最高次項(xiàng)系數(shù)。答案：常數(shù)項(xiàng)是12，最高次項(xiàng)系數(shù)是-2。13.多項(xiàng)式\(B(x)=x^n+2x^{n-1}+3x^{n-2}+\ldots+nx+n\)的次數(shù)是\(n\)，求出當(dāng)\(n=3\)時(shí)，該多項(xiàng)式的表達(dá)式。答案：當(dāng)\(n=3\)時(shí)，多項(xiàng)式\(B(x)\)的表達(dá)式為\(x^3+2x^2+3x+3\)。14.已知多項(xiàng)式\(C(x)=ax^3+bx^2+cx+d\)的系數(shù)\(a\)，\(b\)，\(c\)，\(d\)分別是1，-3，2，-6，求出該多項(xiàng)式的次數(shù)和常數(shù)項(xiàng)。答案：該多項(xiàng)式的次數(shù)是3，常數(shù)項(xiàng)是-6。15.多項(xiàng)式\(D(x)