7.3E: Mazoezi

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Mazoezi hufanya kamili

Kutambua Mkakati wa awali kwa sababu Polynomials kabisa

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

Zoezi 1

$10q^2+50$
$a^2−5a−14$
$uv+2u+3v+6$

Jibu

sababu ya GCF, binomial
tengua FOIL
sababu kwa kikundi

Zoezi la 2

$n^2+10n+24$
$8u^2+16$
$pq+5p+2q+10$

Zoezi la 3

$x^2+4x−21$
$ab+10b+4a+40$
$6c^2+24$

Jibu

tengua FOIL
sababu kwa kikundi
sababu ya GCF, binomial

Zoezi la 4

$20x^2+100$
$uv+6u+4v+24$
$y^2−8y+15$

Factor Trinomials ya fomu$ax^2+bx+c$ na GCF

Katika mazoezi yafuatayo, factor kabisa.

Zoezi 5

$5x^2+35x+30$

Jibu: $5(x+1)(x+6)$

Zoezi la 6

$12s^2+24s+12$

Zoezi la 7

$2z^2−2z−24$

Jibu: $2(z−4)(z+3)$

Zoezi 8

$3u^2−12u−36$

Zoezi la 9

$7v^2−63v+56$

Jibu: $7(v−1)(v−8)$

Zoezi 10

$5w^2−30w+45$

Zoezi 11

$p^3−8p^2−20p$

Jibu: $p(p−10)(p+2)$

Zoezi 12

$q^3−5q^2−24q$

Zoezi 13

$3m^3−21m^2+30m$

Jibu: $3m(m−5)(m−2)$

Zoezi 14

$11n^3−55n^2+44n$

Zoezi 15

$5x^4+10x^3−75x^2$

Jibu: $5x^{2}(x−3)(x+5)$

Zoezi 16

$6y^4+12y^3−48y^2$

Factor Trinomials Kutumia Jaribio na Hitilafu

Katika mazoezi yafuatayo, sababu.

Zoezi 17

$2t^2+7t+5$

Jibu: $(2t+5)(t+1)$

Zoezi 18

$5y^2+16y+11$

Zoezi la 19

$11x^2+34x+3$

Jibu: $(11x+1)(x+3)$

Zoezi la 20

$7b^2+50b+7$

Zoezi 21

$4w^2−5w+1$

Jibu: $(4w−1)(w−1)$

Zoezi la 22

$5x^2−17x+6$

Zoezi 23

$6p^2−19p+10$

Jibu: $(3p−2)(2p−5)$

Zoezi 24

$21m^2−29m+10$

Zoezi 25

$4q^2−7q−2$

Jibu: $(4q+1)(q−2)$

Zoezi 26

$10y^2−53y−11$

Zoezi 27

$4p^2+17p−15$

Jibu: $(4p−3)(p+5)$

Zoezi 28

$6u^2+5u−14$

Zoezi 29

$16x^2−32x+16$

Jibu: $16(x−1)(x−1)$

Zoezi 30

$81a^2+153a−18$

Zoezi 31

$30q^3+140q^2+80q$

Jibu: $10q(3q+2)(q+4)$

Zoezi 32

$5y^3+30y^2−35y$

Factor Trinomials kutumia 'ac' Njia

Katika mazoezi yafuatayo, sababu.

Zoezi la 33

$5n^2+21n+4$

Jibu: $(5n+1)(n+4)$

Zoezi 34

$8w^2+25w+3$

Zoezi 35

$9z^2+15z+4$

Jibu: $(3z+1)(3z+4)$

Zoezi 36

$3m^2+26m+48$

Zoezi 37

$4k^2−16k+15$

Jibu: $(2k−3)(2k−5)$

Zoezi 38

$4q^2−9q+5$

Zoezi 39

$5s^2−9s+4$

Jibu: $(5s−4)(s−1)$

Zoezi 40

$4r^2−20r+25$

Zoezi 41

$6y^2+y−15$

Jibu: $(3y+5)(2y−3)$

Zoezi 42

$6p^2+p−22$

Zoezi 43

$2n^2−27n−45$

Jibu: $(2n+3)(n−15)$

Zoezi 44

$12z^2−41z−11$

Zoezi 45

$3x^2+5x+4$

Jibu: mkuu

Zoezi 46

$4y^2+15y+6$

Zoezi 47

$60y^2+290y−50$

Jibu: $10(6y−1)(y+5)$

Zoezi 48

$6u^2−46u−16$

Zoezi 49

$48z^3−102z^2−45z$

Jibu: $3z(8z+3)(2z−5)$

Zoezi 50

$90n^3+42n^2−216n$

Zoezi 51

$16s^2+40s+24$

Jibu: $8(2s+3)(s+1)$

Zoezi 52

$24p^2+160p+96$

Zoezi 53

$48y^2+12y−36$

Jibu: $12(4y−3)(y+1)$

Zoezi 54

$30x^2+105x−60$

Mazoezi ya mchanganyiko

Katika mazoezi yafuatayo, sababu.

Zoezi 55

$12y^2−29y+14$

Jibu: $(4y−7)(3y−2)$

Zoezi 56

$12x^2+36y−24z$

Zoezi 57

$a^2−a−20$

Jibu: $(a−5)(a+4)$

Zoezi 58

$m^2−m−12$

Zoezi 59

$6n^2+5n−4$

Jibu: $(2n−1)(3n+4)$

Zoezi 60

$12y^2−37y+21$

Zoezi 61

$2p^2+4p+3$

Jibu: mkuu

Zoezi 62

$3q^2+6q+2$

Zoezi 63

$13z^2+39z−26$

Jibu: $13(z^2+3z−2)$

Zoezi 64

$5r^2+25r+30$

Zoezi 65

$x^2+3x−28$

Jibu: $(x+7)(x−4)$

Zoezi 66

$6u^2+7u−5$

Zoezi 67

$3p^2+21p$

Jibu: $3p(p+7)$

Zoezi 68

$7x^2−21x$

Zoezi 69

$6r^2+30r+36$

Jibu: $6(r+2)(r+3)$

Zoezi 70

$18m^2+15m+3$

Zoezi 71

$24n^2+20n+4$

Jibu: $4(2n+1)(3n+1)$

Zoezi 72

$4a^2+5a+2$

Zoezi 73

$x^2+2x−24$

Jibu: $(x+6)(x−4)$

Zoezi 74

$2b^2−7b+4$

kila siku Math

Zoezi 75

Urefu wa roketi ya toy Urefu wa roketi ya toy ilizinduliwa kwa kasi ya kwanza ya$80$ miguu kwa pili kutoka kwenye balcony ya jengo la ghorofa ni kuhusiana na idadi ya sekunde$t$, kwa kuwa inazinduliwa na trinomial$−16t^2+80t+96$. Sababu hii trinomial.

Jibu: $−16(t−6)(t+1)$

Zoezi 76

Urefu wa mpira beach urefu wa mpira beach kuchafuka up na kasi ya awali ya$12$ miguu kwa sekunde kutoka urefu wa$4$ miguu ni kuhusiana na idadi ya sekunde$t$,, tangu ni kuchafuka na trinomial$−16t^2+12t+4$. Sababu hii trinomial.

Mazoezi ya kuandika

Zoezi 77

Orodha, kwa utaratibu, hatua zote unazochukua wakati wa kutumia “$ac$” njia ya kuzingatia trinomial ya fomu$ax^2+bx+c$.

Jibu: Majibu yanaweza kutofautiana.

Zoezi 78

Njia ya “$ac$” inafanana na njia ya “kufuta FOIL”? Je, ni tofauti gani?

Zoezi 79

Maswali ni nini, ili, kwamba unajiuliza unapoanza kuzingatia polynomial? Unahitaji kufanya nini kama matokeo ya jibu kwa kila swali?

Jibu: Majibu yanaweza kutofautiana.

Zoezi 80

Katika karatasi yako kuteka chati kwamba muhtasari mkakati factoring. Jaribu kufanya hivyo bila kuangalia kitabu. Unapokamilika, angalia nyuma kwenye kitabu ili uimalize au uhakikishe.

Self Check

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

$Jedwali hili lina kauli zifuatazo zote kutanguliwa na “Naweza...”. Mstari wa kwanza ni “kutambua mkakati wa awali kwa sababu polynomials kabisa”. Mstari wa pili ni “trinomials ya sababu ya fomu a x ^ 2 + b x + c na GCF”. Mstari wa tatu ni “trinomials sababu kutumia jaribio na hitilafu”. Na mstari wa nne ni “trinomials sababu kutumia “ac” njia”. Katika nguzo kando ya kauli hizi ni vichwa, “kwa ujasiri”, “kwa msaada fulani”, na “Hakuna-siipati!”.$

b Orodha hii inakuambia nini kuhusu ujuzi wako wa sehemu hii? Ni hatua gani utachukua ili kuboresha?