6.6E: Mazoezi

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Mazoezi hufanya kamili

Katika mazoezi yafuatayo, kugawanya kila polynomial na monomial.

Zoezi 1

$\dfrac{45y+36}{9}$

Zoezi la 2

$\dfrac{30b+75}{5}$

Jibu: $6b+15$

Zoezi la 3

$\dfrac{8d^2−4d}{2}$

Zoezi la 4

$\dfrac{42x^2−14x}{7}$

Jibu: $6x^2−2x$

Zoezi 5

$(16y^2−20y)÷4y$

Zoezi la 6

$(55w^2−10w)÷5w$

Jibu: $11w−2$

Zoezi la 7

$(9n^4+6n^3)÷3n$

Zoezi 8

$(8x^3+6x^2)÷2x$

Jibu: $4x^2+3x$

Zoezi la 9

$\dfrac{18y^2−12y}{−6}$

Zoezi 10

$\dfrac{20b^2−12b}{−4}$

Jibu: $−5b^2+3b$

Zoezi 11

$\dfrac{35a^4+65a^2}{−5}$

Zoezi 12

$\dfrac{51m^4+72m^3}{−3}$

Jibu: $−17m^4−24m^3$

Zoezi 13

$\dfrac{310y^4−200y^3}{5y^2}$

Zoezi 14

$\dfrac{412z^8−48z^5}{4z^3}$

Jibu: $103z^5−12z^2$

Zoezi 15

$\dfrac{46x^3+38x^2}{2x^2}$

Zoezi 16

$\dfrac{51y^4+42y^2}{3y^2}$

Jibu: $17y^2+14$

Zoezi 17

$(24p^2−33p)÷(−3p)$

Zoezi 18

$(35x^4−21x)÷(−7x)$

Jibu: $−5x^3+3$

Zoezi la 19

$(63m^4−42m^3)÷(−7m^2)$

Zoezi la 20

$(48y^4−24y^3)÷(−8y^2)$

Jibu: $−6y^2+3y$

Zoezi 21

$(63a^{2}b^3+72ab^4)÷(9ab)$

Zoezi la 22

$(45x^{3}y^4+60xy^2)÷(5xy)$

Jibu: $9x^{2}y^3+12y$

Zoezi 23

$\dfrac{52p^{5}q^4+36p^{4}q^3−64p^{3}q^2}{4p^{2}q}$

Zoezi 24

$\dfrac{49c^{2}d^2−70c^{3}d^3−35c^{2}d}{47cd^2}$

Jibu: $7c−10c^{2}d−5cd^2$

Zoezi 25

$\dfrac{66x^{3}y^2−110x^{2}y^3−44x^{4}y^3}{11x^{2}y^2}$

Zoezi 26

$\dfrac{72r^{5}s^2+132r^{4}s^3−96r^{3}s^5}{12r^{2}s^2}$

Jibu: $6r^3+11r^{2}s−8rs^3$

Zoezi 27

$\dfrac{4w^2+2w−5}{2w}$

Zoezi 28

$\dfrac{12q^2+3q−1}{3q}$

Jibu: $4q+1−\dfrac{1}{3q}$

Zoezi 29

$\dfrac{10x^2+5x−4}{−5x}$

Zoezi 30

$\dfrac{20y^2+12y−1}{−4y}$

Jibu: $−5y−3+\dfrac{1}{4y}$

Zoezi 31

$\dfrac{36p^3+18p^2−12p}{6p^2}$

Zoezi 32

$\dfrac{63a^3−108a^2+99a}{9a^2}$

Jibu: $7a−12+\dfrac{11}{a}$

Gawanya Polynomial na Binomial

Katika mazoezi yafuatayo, kugawanya kila polynomial na binomial.

Zoezi la 33

$(y^2+7y+12)÷(y+3)$

Zoezi 34

$(d^2+8d+12)÷(d+2)$

Jibu: $d+6$

Zoezi 35

$(x^2−3x−10)÷(x+2)$

Zoezi 36

$(a^2−2a−35)÷(a+5)$

Jibu: $a−7$

Zoezi 37

$(t^2−12t+36)÷(t−6)$

Zoezi 38

$(x^2−14x+49)÷(x−7)$

Jibu: $x−7$

Zoezi 39

$(6m^2−19m−20)÷(m−4)$

Zoezi 40

$(4x^2−17x−15)÷(x−5)$

Jibu: $4x+3$

Zoezi 41

$(q^2+2q+20)÷(q+6)$

Zoezi 42

$(p^2+11p+16)÷(p+8)$

Jibu: $p+3−\dfrac{8}{p+8}$

Zoezi 43

$(y^2−3y−15)÷(y−8)$

Zoezi 44

$(x^2+2x−30)÷(x−5)$

Jibu: $x+7+\dfrac{5}{x−5}$

Zoezi 45

$(3b^3+b^2+2)÷(b+1)$

Zoezi 46

$(2n^3−10n+28)÷(n+3)$

Jibu: $2n^2−6n+8 + \frac{4}{n+3}$

Zoezi 47

$(2y^3−6y−36)÷(y−3)$

Zoezi 48

$(7q^3−5q−2)÷(q−1)$

Jibu: $7q^2+7q+2$

Zoezi 49

$(z^3+1)÷(z+1)$

Zoezi 50

$(m^3+1000)÷(m+10)$

Jibu: $m^2−10m+100$

Zoezi 51

$(a^3−125)÷(a−5)$

Zoezi 52

$(x^3−216)÷(x−6)$

Jibu: $x^2+6x+36$

Zoezi 53

$(64x^3−27)÷(4x−3)$

Zoezi 54

$(125y^3−64)÷(5y−4)$

Jibu: $25y^2+20x+16$

kila siku Math

Zoezi 55

Wastani wa gharama Picha Plus hutoa albamu za digital. Wastani wa gharama ya kampuni (kwa dola) kufanya albamu x hutolewa kwa kujieleza$\dfrac{7x+500}{x}$

Pata quotient kwa kugawa nambari na denominator.
Gharama ya wastani (kwa dola) itakuwa kuzalisha albamu 20?

Zoezi 56

Handshakes Katika mkutano wa kampuni, kila mfanyakazi hupiga mikono na kila mfanyakazi mwingine. Idadi ya handshakes hutolewa kwa usemi$\dfrac{n^2−n}{2}$ nn inawakilisha idadi ya wafanyakazi. Je, kuna mikono ngapi ikiwa kuna wafanyakazi 10 kwenye mkutano?

Jibu: 45

Mazoezi ya kuandika

Zoezi 57

James$48y+6$ anagawanyika kwa njia$6$ hii:$\dfrac{48y+6}{6}=48y$

Zoezi 58

Gawanya$\dfrac{10x^2+x−12}{2x}$ na ueleze kwa maneno jinsi unavyopata kila neno la quotient.

Jibu: Majibu yatatofautiana.

Self Check

ⓐ Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

$Hii ni meza ambayo ina safu tatu na nguzo nne. Katika mstari wa kwanza, ambayo ni mstari wa kichwa, seli zinasoma kutoka kushoto kwenda kulia “Ninaweza...,” “Kwa ujasiri,” “Kwa msaada fulani,” na “Hakuna-Siipati!” Safu ya kwanza chini ya “Naweza...” inasoma “kugawanya polynomial na monomial,” na “ugawanye polynomial na binomial.” Wengine wa seli ni tupu.$

ⓑ Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?