Sura ya 7 Mazoezi Mapitio

Sura ya 7 Mazoezi Mapitio

7.1 Sababu kubwa ya kawaida na Sababu kwa Kundi

Pata sababu kubwa ya kawaida ya maneno mawili au Zaidi

Katika mazoezi yafuatayo, pata sababu kubwa zaidi ya kawaida.

Zoezi 1

42, 60

Jibu

6

Zoezi 2

450, 420

Zoezi la 3

90, 150, 105

Jibu

15

Zoezi 4

60, 294, 630

Sababu ya Sababu kuu ya kawaida kutoka kwa Polynomial

Katika mazoezi yafuatayo, fikiria sababu kubwa zaidi kutoka kwa kila polynomial.

Zoezi 5

$24x−42$

Jibu

$6(4x−7)$

Zoezi 6

$35y+84$

Zoezi la 7

$15m^4+6m^{2}n$

Jibu

$3m^2(5m2+2n)$

Zoezi 8

$24pt^4+16t^7$

Kielelezo kwa Kundi

Katika mazoezi yafuatayo, sababu kwa kikundi.

Zoezi la 9

$ax−ay+bx−by$

Jibu

$(a+b)(x−y)$

Zoezi 10

$x^{2}y−xy^2+2x−2y$

Zoezi 11

$x^2+7x−3x−21$

Jibu

$(x−3)(x+7)$

Zoezi 12

$4x^2−16x+3x−12$

Zoezi 13

$m^3+m^2+m+1$

Jibu

$(m^2+1)(m+1)$

Zoezi 14

$5x−5y−y+x$

7.2 Factor Trinomials ya fomu$x^2+bx+c$

Sababu Trinomials ya Fomu$x^2+bx+c$

Katika mazoezi yafuatayo, fanya kila trinomial ya fomu$x^2+bx+c$

Zoezi 15

$u^2+17u+72$

Jibu

$(u+8)(u+9)$

Zoezi 16

$a^2+14a+33$

Zoezi 17

$k^2−16k+60$

Jibu

$(k−6)(k−10)$

Zoezi 18

$r^2−11r+28$

Zoezi la 19

$y^2+6y−7$

Jibu

$(y+7)(y−1)$

Zoezi la 20

$m^2+3m−54$

Zoezi 21

$s^2−2s−8$

Jibu

$(s−4)(s+2)$

Zoezi la 22

$x^2−3x−10$

Sababu Trinomials ya Fomu$x^2+bxy+cy^2$

Katika mifano ifuatayo, factor kila trinomial ya fomu$x^2+bxy+cy^2$

Zoezi 23

$x^2+12xy+35y^2$

Jibu

$(x+5y)(x+7y)$

Zoezi 24

$u^2+14uv+48v^2$

Zoezi 25

$a^2+4ab−21b^2$

Jibu

$(a+7b)(a−3b)$

Zoezi 26

$p^2−5pq−36q^2$

7.3 Kuzingatia Trinomials ya fomu$ax^2+bx+c$

Kutambua Mkakati wa awali kwa sababu Polynomials kabisa

Katika mazoezi yafuatayo, tambua njia bora ya kutumia ili kuzingatia kila polynomial.

Zoezi 27

$y^2−17y+42$

Jibu

tengua FOIL

Zoezi 28

$12r^2+32r+5$

Zoezi 29

$8a^3+72a$

Jibu

Sababu ya GCF

Zoezi 30

$4m−mn−3n+12$

Sababu Trinomials ya Fomu$ax^2+bx+c$ with a GCF

Katika mazoezi yafuatayo, factor kabisa.

Zoezi 31

$6x^2+42x+60$

Jibu

$6(x+2)(x+5)$

Zoezi 32

$8a^2+32a+24$

Zoezi la 33

$3n^4−12n^3−96n^2$

Jibu

$3n^{2}(n−8)(n+4)$

Zoezi 34

$5y^4+25y^2−70y$

Sababu Trinomials Kutumia Njia ya “ac”

Katika mazoezi yafuatayo, sababu.

Zoezi 35

$2x^2+9x+4$

Jibu

$(x+4)(2x+1)$

Zoezi 36

$3y^2+17y+10$

Zoezi 37

$18a^2−9a+1$

Jibu

$(3a−1)(6a−1)$

Zoezi 38

$8u^2−14u+3$

Zoezi 39

$15p^2+2p−8$

Jibu

$(5p+4)(3p−2)$

Zoezi 40

$15x^2+6x−2$

Zoezi 41

$40s^2−s−6$

Jibu

$(5s−2)(8s+3)$

Zoezi 42

$20n^2−7n−3$

Factor Trinomials na GCF Kutumia “ac” Njia

Katika mazoezi yafuatayo, sababu.

Zoezi 43

$3x^2+3x−36$

Jibu

$3(x+4)(x−3)$

Zoezi 44

$4x^2+4x−8$

Zoezi 45

$60y^2−85y−25$

Jibu

$5(4y+1)(3y−5)$

Zoezi 46

$18a^2−57a−21$

7.4 Factoring Maalum Bidhaa

Factor Perfect Square trinomials

Katika mazoezi yafuatayo, sababu.

Zoezi 47

$25x^2+30x+9$

Jibu

$(5x+3)^2$

Zoezi 48

$16y^2+72y+81$

Zoezi 49

$36a^2−84ab+49b^2$

Jibu

$(6a−7b)^2$

Zoezi 50

$64r^2−176rs+121s^2$

Zoezi 51

$40x^2+360x+810$

Jibu

$10(2x+9)^2$

Zoezi 52

$75u^2+180u+108$

Zoezi 53

$2y^3−16y^2+32y$

Jibu

$2y(y−4)^2$

Zoezi 54

$5k^3−70k^2+245k$

Sababu tofauti ya Viwanja

Katika mazoezi yafuatayo, sababu.

Zoezi 55

$81r^2−25$

Jibu

$(9r−5)(9r+5)$

Zoezi 56

$49a^2−144$

Zoezi 57

$169m^2−n^2$

Jibu

$(13m+n)(13m−n)$

Zoezi 58

$64x^2−y^2$

Zoezi 59

$25p^2−1$

Jibu

$(5p−1)(5p+1)$

Zoezi 60

$1−16s^2$

Zoezi 61

$9−121y^2$

Jibu

$(3+11y)(3−11y)$

Zoezi 62

$100k^2−81$

Zoezi 64

$20x^2−125$

Jibu

$5(2x−5)(2x+5)$

Zoezi 64

$18y^2−98$

Zoezi 65

$49u^3−9u$

Jibu

$u(7u+3)(7u−3)$

Zoezi 66

$169n^3−n$

Kiasi cha Kiasi na Tofauti za Cubes

Katika mazoezi yafuatayo, sababu.

Zoezi 67

$a^3−125$

Jibu

$(a−5)(a^2+5a+25)$

Zoezi 68

$b^3−216$

Zoezi 69

$2m^3+54$

Jibu

$2(m+3)(m^2−3m+9)$

Zoezi 70

$81x^3+3$

Mkakati Mkuu wa 7.5 wa kuzingatia Polynomials

Kutambua na Tumia Njia sahihi ya Kufanya Kipolynomial Kikamilifu

Katika mazoezi yafuatayo, factor kabisa.

Zoezi 71

$24x^3+44x^2$

Jibu

$4x^{2}(6x+11)$

Zoezi 72

$24a^4−9a^3$

Zoezi 73

$16n^2−56mn+49m^2$

Jibu

$(4n−7m)^2$

Zoezi 74

$6a^2−25a−9$

Zoezi 75

$5r^2+22r−48$

Jibu

(r+6) (5r-8)

Zoezi 76

$5u^4−45u^2$

Zoezi 77

$n^4−81$

Jibu

$(n^2+9)(n+3)(n−3)$

Zoezi 78

$64j^2+225$

Zoezi 79

$5x^2+5x−60$

Jibu

$5(x−3)(x+4)$

Zoezi 80

$b^3−64$

Zoezi 81

$m^3+125$

Jibu

$(m+5)(m^2−5m+25)$

Zoezi 82

$2b^2−2bc+5cb−5c^2$

7.6 Ulinganifu wa Quadratic

Tumia mali ya Bidhaa ya Zero

Katika mazoezi yafuatayo, tatua.

Zoezi 83

$(a−3)(a+7)=0$

Jibu

$a=3$,$a=−7$

Zoezi 84

$(b−3)(b+10)=0$

Zoezi 85

$3m(2m−5)(m+6)=0$

Jibu

$m=0$,$m=−6$,$m=\frac{5}{2}$

Zoezi 86

$7n(3n+8)(n−5)=0$

Tatua Ulinganisho wa Quadratic kwa kuzingatia

Katika mazoezi yafuatayo, tatua.

Zoezi 87

$x^2+9x+20=0$

Jibu

$x=−4$,$x=−5$

Zoezi 88

$y^2−y−72=0$

Zoezi 89

$2p^2−11p=40$

Jibu

$p=−\frac{5}{2}$, p=8

Zoezi 90

$q^3+3q^2+2q=0$

Zoezi 91

$144m^2−25=0$

Jibu

$m=\frac{5}{12}$,$m=−\frac{5}{12}$

Zoezi 92

$4n^2=36$

Kutatua Maombi yanayotokana na equations Quadratic

Katika mazoezi yafuatayo, tatua.

Zoezi 93

Bidhaa ya namba mbili za mfululizo ni 462.

Jibu

-21, -22

21, 22

Zoezi 94

Eneo la patio yenye umbo la mstatili 400 futi za mraba. Urefu wa patio ni futi 99 zaidi ya upana wake. Pata urefu na upana.

Mazoezi mtihani

Katika mazoezi yafuatayo, pata sababu kubwa ya kawaida katika kila kujieleza.

Zoezi 95

$14y−42$

Jibu

$7(y−6)$

Zoezi 96

$−6x^2−30x$

Zoezi 97

$80a^2+120a^3$

Jibu

$40a^{2}(2+3a)$

Zoezi 98

$5m(m−1)+3(m−1)$

Katika mazoezi yafuatayo, factor kabisa.

Zoezi 99

$x^2+13x+36$

Jibu

$(x+7)(x+6)$

Zoezi 100

$p^2+pq−12q^2$

Zoezi 101

$3a^3−6a^2−72a$

Jibu

$3a(a+4)(a-6)$

Zoezi 102

$s^2−25s+84$

Zoezi 103

$5n^2+30n+45$

Jibu

$5(n+3)^2$

Zoezi 104

$64y^2−49$

Zoezi 105

$xy−8y+7x−56$

Jibu

$(x−8)(y+7)$

Zoezi 106

$40r^2+810$

Zoezi 107

$9s^2−12s+4$

Jibu

$(3s−2)^2$

Zoezi 1008

$n^2+12n+36$

Zoezi 109

$100−a^2$

Jibu

$(10−a)(10+a)$

Zoezi 110

$6x^2−11x−10$

Zoezi 111

$3x^2−75y^2$

Jibu

$3(x+5y)(x−5y)$

Zoezi 112

$c^3−1000d^3$

Zoezi 113

$ab−3b−2a+6$

Jibu

$(a−3)(b−2)$

Zoezi 114

$6u^2+3u−18$

Zoezi 115

$8m^2+22m+5$

Jibu

$(4m+1)(2m+5)$

Katika mazoezi yafuatayo, tatua.

Zoezi 116

$x^2+9x+20=0$

Zoezi 117

$y^2=y+132$

Jibu

$y=−11$,$y=12$

Zoezi 118

$5a^2+26a=24$

Zoezi 119

$9b^2−9=0$

Jibu

$b=1$,$b=−1$

Zoezi 120

$16−m^2=0$

Zoezi 121

$4n^2+19n+21=0$

Jibu

$n=−\frac{7}{4}$, n=-3

Zoezi 122

$(x−3)(x+2)=6$

Zoezi 123

Bidhaa ya integers mbili mfululizo ni 156.

Jibu

12 na 13; -13 na -12

Zoezi 124

Eneo la kitanda cha mstatili ni inchi za mraba 168. Urefu wake ni urefu wa inchi mbili kuliko upana. Pata urefu na upana wa mahali pa mahali.