7.2E: Mazoezi

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Mazoezi hufanya kamili

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

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

Zoezi 1

$x^2+4x+3$

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

Zoezi la 2

$y^2+8y+7$

Zoezi la 3

$m^2+12m+11$

Jibu: $(m+1)(m+11)$

Zoezi la 4

$b^2+14b+13$

Zoezi 5

$a^2+9a+20$

Jibu: $(a+4)(a+5)$

Zoezi la 6

$m^2+7m+12$

Zoezi la 7

$p^2+11p+30$

Jibu: $(p+5)(p+6)$

Zoezi 8

$w^2+10w+21$

Zoezi la 9

$n^2+19n+48$

Jibu: $(n+3)(n+16)$

Zoezi 10

$b^2+14b+48$

Zoezi 11

$a^2+25a+100$

Jibu: $(a+5)(a+20)$

Zoezi 12

$u^2+101u+100$

Zoezi 13

$x^2−8x+12$

Jibu: $(x−2)(x−6)$

Zoezi 14

$q^2−13q+36$

Zoezi 15

$y^2−18y+45$

Jibu: $(y−3)(y−15)$

Zoezi 16

$m^2−13m+30$

Zoezi 17

$x^2−8x+7$

Jibu: $(x−1)(x−7)$

Zoezi 18

$y^2−5y+6$

Zoezi la 19

$p^2+5p−6$

Jibu: $(p−1)(p+6)$

Zoezi la 20

$n^2+6n−7$

Zoezi 21

$y^2−6y−7$

Jibu: $(y+1)(y−7)$

Zoezi la 22

$v^2−2v−3$

Zoezi 23

$x^2−x−12$

Jibu: $(x−4)(x+3)$

Zoezi 24

$r^2−2r−8$

Zoezi 25

$a^2−3a−28$

Jibu: $(a−7)(a+4)$

Zoezi 26

$b^2−13b−30$

Zoezi 27

$w^2−5w−36$

Jibu: $(w−9)(w+4)$

Zoezi 28

$t^2−3t−54$

Zoezi 29

$x^2+x+5$

Jibu: mkuu

Zoezi 30

$x^2−3x−9$

Zoezi 31

$8−6x+x^2$

Jibu: $(x−4)(x−2)$

Zoezi 32

$7x+x^2+6$

Zoezi la 33

$x^2−12−11x$

Jibu: $(x−12)(x+1)$

Zoezi 34

$−11−10x+x^2$

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

Katika mazoezi yafuatayo, fanya kila trinomial ya fomu$x^2+bxy+cy^2$

Zoezi la 33

$p^2+3pq+2q^2$

Jibu: $(p+q)(p+2q)$

Zoezi 34

$m^2+6mn+5n^2$

Zoezi 35

$r^2+15rs+36s^2$

Jibu: $(r+3s)(r+12s)$

Zoezi 36

$u^2+10uv+24v^2$

Zoezi 37

$m^2−12mn+20n^2$

Jibu: $(m−2n)(m−10n)$

Zoezi 38

$p^2−16pq+63q^2$

Zoezi 39

$x^2−2xy−80y^2$

Jibu: $(x+8y)(x−10y)$

Zoezi 40

$p^2−8pq−65q^2$

Zoezi 41

$m^2−64mn−65n^2$

Jibu: $(m+n)(m−65n)$

Zoezi 42

$p^2−2pq−35q^2$

Zoezi 43

$a^2+5ab−24b^2$

Jibu: $(a+8b)(a−3b)$

Zoezi 44

$r^2+3rs−28s^2$

Zoezi 45

$x^2−3xy−14y^2$

Jibu: mkuu

Zoezi 46

$u^2−8uv−24v^2$

Zoezi 47

$m^2−5mn+30n^2$

Jibu: mkuu

Zoezi 48

$c^2−7cd+18d^2$

Mazoezi ya mchanganyiko

Katika mazoezi yafuatayo, fikiria kila kujieleza.

Zoezi 49

$u^2−12u+36$

Jibu: $(u−6)(u−6)$

Zoezi 50

$w^2+4w−32$

Zoezi 51

$x^2−14x−32$

Jibu: $(x+2)(x−16)$

Zoezi 52

$y^2+41y+40$

Zoezi 53

$r^2−20rs+64s^2$

Jibu: $(r−4s)(r−16s)$

Zoezi 54

$x^2−16xy+64y^2$

Zoezi 55

$k^2+34k+120$

Jibu: $(k+4)(k+30)$

Zoezi 56

$m^2+29m+120$

Zoezi 57

$y^2+10y+15$

Jibu: mkuu

Zoezi 58

$z^2−3z+28$

Zoezi 59

$m^2+mn−56n^2$

Jibu: $(m+8n)(m−7n)$

Zoezi 60

$q^2−29qr−96r^2$

Zoezi 61

$u^2−17uv+30v^2$

Jibu: $(u−15v)(u−2v)$

Zoezi 62

$m^2−31mn+30n^2$

Zoezi 63

$c^2−8cd+26d^2$

Jibu: mkuu

Zoezi 64

$r^2+11rs+36s^2$

kila siku Math

Zoezi 65

Integers mfululizo Deirdre ni kufikiri ya integers mbili mfululizo ambao bidhaa ni 56. Trinomial$x^2+x−56$ inaelezea jinsi namba hizi zinahusiana. Sababu ya trinomial.

Jibu: $(x+8)(x−7)$

Zoezi 66

Integers mfululizo Deshawn ni kufikiri ya integers mbili mfululizo ambao bidhaa ni 182. Trinomial$x^2+x−182$ inaelezea jinsi namba hizi zinahusiana. Factor trinomial inaelezea jinsi namba hizi zinahusiana. Sababu ya trinomial.

Mazoezi ya kuandika

Zoezi 67

Trinomials nyingi za$x^2+bx+c$ sababu ya fomu katika bidhaa za binomials mbili$(x+m)(x+n)$. Eleza jinsi unavyopata maadili ya$m$ na$n$.

Jibu: Majibu inaweza kutofautiana

Zoezi 68

Je, unaamuaje ikiwa unatumia ishara za pamoja au za minus katika mambo ya binomial ya trinomial ya fomu$x^2+bx+c$ ambapo$b$ na$c$ inaweza kuwa namba nzuri au hasi?

Zoezi 69

Je factored$x^2−x−20$ kama$(x+5)(x−4)$. Bill factored kama$(x+4)(x−5)$. Phil factored kama$(x−5)(x−4)$. Nani ni sahihi? Eleza kwa nini wengine wawili ni makosa.

Jibu: Majibu inaweza kutofautiana

Zoezi 70

Angalia Mfano, ambapo sisi factored$y^2+17y+60$. Tulifanya meza kuorodhesha jozi zote za sababu za 60 na kiasi chao. Je, kupata aina hii ya meza na manufaa? Kwa nini au kwa nini?

Self Check

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

$Jedwali hili lina kauli zifuatazo zote kutanguliwa na “Naweza...”. Ya kwanza ni “trinomials ya sababu ya fomu x ^ 2 +b x + c”. Ya pili ni “trinomials sababu ya fomu x ^ 2 + b x y + c y ^ 2”. Katika nguzo kando ya kauli hizi ni vichwa, “kwa ujasiri”, “kwa msaada fulani”, na “Hakuna-siipati!”.$

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