4.4 整式 浙教版數(shù)學(xué)七年級(jí)上冊(cè)同步練習(xí)(解析版)

第4章代數(shù)式4.4整式基礎(chǔ)過(guò)關(guān)全練知識(shí)點(diǎn)1單項(xiàng)式1.下列式子中,屬于單項(xiàng)式的有()1-2x,2x2+x-1,0,3(a-b),-15a,1x,A.1個(gè)B.2個(gè)C.3個(gè)D.4個(gè)2.下列說(shuō)法正確的是()A.2xB.單項(xiàng)式-x2C.2x2y的系數(shù)、次數(shù)都是2D.-x4y是五次單項(xiàng)式3.(2022浙江金華義烏賓王中學(xué)月考)已知單項(xiàng)式5x2ya的次數(shù)是5,則a的值是()A.3 B.4C.5 D.64.(2022浙江杭州期末)單項(xiàng)式-3x2y的次數(shù)是.

知識(shí)點(diǎn)2多項(xiàng)式5.在代數(shù)式x2+5,-1,x2-3x+2,π,5x,x2+1x+5中,多項(xiàng)式有A.2個(gè) B.3個(gè)C.4個(gè) D.6個(gè)6.多項(xiàng)式a2-a+2是()A.二次二項(xiàng)式 B.二次三項(xiàng)式C.三次二項(xiàng)式 D.三次三項(xiàng)式7.多項(xiàng)式x3-2x2-3的最高次項(xiàng)的系數(shù)是,常數(shù)項(xiàng)是.

8.試寫(xiě)出兩個(gè)只含有字母x、y的多項(xiàng)式,且滿足下列條件:(1)是六次三項(xiàng)式;(2)每一項(xiàng)的系數(shù)均為1或-1;(3)不含常數(shù)項(xiàng);(4)每一項(xiàng)必須同時(shí)含有字母x、y.知識(shí)點(diǎn)3整式9.下列說(shuō)法正確的是()A.單項(xiàng)式2x2y3B.3x+2x-1C.多項(xiàng)式3x2y-5x2y2-2xy的次數(shù)是4D.xy-10.下列式子中,哪些是整式?哪些是單項(xiàng)式?哪些是多項(xiàng)式?2x,3a,-2x+x2,-53x2y,a2+ab+b2,x+2能力提升全練11.如果2x3ym+(n-2)x是關(guān)于x,y的五次二項(xiàng)式,那么關(guān)于m,n的值正確的是()A.m=3,n≠2 B.m=2,n=3C.m=3,n=2 D.m=2,n≠212.已知關(guān)于x、y的多項(xiàng)式(a+b)x5+(a-3)x3-2(b+2)x2+2ax+1中不含x3和x2項(xiàng),則當(dāng)x=-1時(shí),這個(gè)多項(xiàng)式的值為.

13.按一定規(guī)律排列的單項(xiàng)式:3a2,8a5,15a8,24a11,…,則第9個(gè)單項(xiàng)式是.

14.若多項(xiàng)式ab|m-1|+(n-1)a3b3+1是關(guān)于a,b的五次多項(xiàng)式,則m=.

素養(yǎng)探究全練15.[邏輯推理]多項(xiàng)式4x2-5x+9與2x2-ax+1的一次項(xiàng)系數(shù)相同,多項(xiàng)式x2-3x與bx2-3x+6的二次項(xiàng)系數(shù)互為相反數(shù),試求代數(shù)式b2-15ab的值16.[數(shù)學(xué)運(yùn)算]已知數(shù)a,b在數(shù)軸上的位置如圖所示,且a-|b-a|=-3,若多項(xiàng)式(a+2b)x3-x2+x-b是關(guān)于x的二次三項(xiàng)式,求a與b的平方和.

答案全解全析基礎(chǔ)過(guò)關(guān)全練1.B1-2x,2x2+x-1,3(a-b),1+x2中都有加(或減)法運(yùn)算,不是單項(xiàng)式.1x的分母中含有字母,不是單項(xiàng)式.0和-15a是單項(xiàng)式,2.D根據(jù)單項(xiàng)式的概念及單項(xiàng)式的次數(shù)、系數(shù)的定義進(jìn)行判斷.2x-y2中有減法運(yùn)算,不是單項(xiàng)式,故選項(xiàng)A錯(cuò)誤;單項(xiàng)式-x2y2的系數(shù)是-12,故選項(xiàng)B錯(cuò)誤;2x2y的系數(shù)是2,次數(shù)是3,故選項(xiàng)C錯(cuò)誤3.A因?yàn)閱雾?xiàng)式5x2ya的次數(shù)是5,所以2+a=5,所以a=3.4.3解析單項(xiàng)式-3x2y的次數(shù)是2+1=3.5.Ax2+5是多項(xiàng)式;-1是單項(xiàng)式;x2-3x+2是多項(xiàng)式;π是單項(xiàng)式;5x與x2+1x+5的分母中含有字母,不是多項(xiàng)式.故多項(xiàng)式有6.B多項(xiàng)式a2-a+2由a2,-a,2三項(xiàng)組成,其中a2是二次項(xiàng),-a是一次項(xiàng),2是常數(shù)項(xiàng),所以它的次數(shù)是2,所以這個(gè)多項(xiàng)式是二次三項(xiàng)式.7.1;-3解析多項(xiàng)式x3-2x2-3由x3,-2x2,-3三項(xiàng)組成,x3是三次項(xiàng),-2x2是二次項(xiàng),-3是常數(shù)項(xiàng),所以最高次項(xiàng)的系數(shù)是1,常數(shù)項(xiàng)是-3.8.解析此題答案不唯一,如:x3y3-x2y4+xy5,-x2y4-xy-xy2等.9.C單項(xiàng)式2x2y3的系數(shù)是23,次數(shù)是2+1=3,所以A錯(cuò)誤;3x+2x-1的分母中含有字母,不是整式,所以B錯(cuò)誤;多項(xiàng)式3x2y-5x2y2-2xy的次數(shù)是4,所以C正確;xy-12中含有減法運(yùn)算10.解析整式:2x,-2x+x2,-53x2y,a2+ab+b2,x單項(xiàng)式:2x,-53x2多項(xiàng)式:-2x+x2,a2+ab+b2,x+2能力提升全練11.D∵2x3ym+(n-2)x是關(guān)于x,y的五次二項(xiàng)式,∴3+m=5,n-2≠0,∴m=2,n≠2.12.-6解析∵多項(xiàng)式不含x3和x2項(xiàng),∴a-3=0,b+2=0,∴a=3,b=-2,當(dāng)x=-1時(shí),原式=-(a+b)-2a+1=-a-b-2a+1=-3a-b+1=-9+2+1=-6.13.99a26解析第1個(gè)單項(xiàng)式是3a2=(22-1)a3×1-1,第2個(gè)單項(xiàng)式是8a5=(32-1)a3×2-1,第3個(gè)單項(xiàng)式是15a8=(42-1)a3×3-1,第4個(gè)單項(xiàng)式是24a11=(52-1)a3×4-1,……∴第9個(gè)單項(xiàng)式是(102-1)a3×9-1=99a26.14.5或-3解析由題意得|m-1|=4,n-1=0,∴m=5或-3,n=1.素養(yǎng)探究全練15.解析因?yàn)槎囗?xiàng)式4x2-5x+9與2x2-ax+1的一次項(xiàng)系數(shù)相同,所以-a=-5,即a=5.因?yàn)槎囗?xiàng)式x2-3x與bx2-3x+6的二次項(xiàng)系數(shù)互為相反數(shù),所以b=-1.所以b2-15ab=(-1)2-116.解析由數(shù)軸