7.5E: Mazoezi

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Mazoezi hufanya kamili

Kutambua na Tumia Njia sahihi ya Kufanya Kipolynomial Kikamilifu

Katika mazoezi yafuatayo, factor kabisa.

Zoezi$\PageIndex{31}$

$10x^4+35x^3$

Jibu: $5x^{3}(2x+7)$

Zoezi$\PageIndex{32}$

$18p^6+24p^3$

Zoezi$\PageIndex{33}$

$y^2+10y−39$

Jibu: $(y−3)(y+13)$

Zoezi$\PageIndex{34}$

$b^2−17b+60$

Zoezi$\PageIndex{35}$

$2n^2+13n−7$

Jibu: $(2n−1)(n+7)$

Zoezi$\PageIndex{36}$

$8x^2−9x−3$

Zoezi$\PageIndex{37}$

$a^5+9a^3$

Jibu: $a^{3}(a^2+9)$

Zoezi$\PageIndex{38}$

$75m^3+12m$

Zoezi$\PageIndex{39}$

$121r^2−s^2$

Jibu: $(11r−s)(11r+s)$

Zoezi$\PageIndex{40}$

$49b^2−36a^2$

Zoezi$\PageIndex{41}$

$8m^2−32$

Jibu: $8(m−2)(m+2)$

Zoezi$\PageIndex{42}$

$36q^2−100$

Zoezi$\PageIndex{43}$

$25w^2−60w+36$

Jibu: $(5w−6)^2$

Zoezi$\PageIndex{44}$

$49b^2−112b+64$

Zoezi$\PageIndex{45}$

$m^2+14mn+49n^2$

Jibu: $(m+7n)^2$

Zoezi$\PageIndex{46}$

$64x^2+16xy+y^2$

Zoezi$\PageIndex{47}$

$7b^2+7b−42$

Jibu: $7(b+3)(b−2)$

Zoezi$\PageIndex{48}$

$3n^2+30n+72$

Zoezi$\PageIndex{49}$

$3x^3−81$

Jibu: $3(x−3)(x^2+3x+9)$

Zoezi$\PageIndex{50}$

$5t^3−40$

Zoezi$\PageIndex{51}$

$k^4−16$

Jibu: $(k−2)(k+2)(k^2+4)$

Zoezi$\PageIndex{52}$

$m^4−81$

Zoezi$\PageIndex{53}$

$15pq−15p+12q−12$

Jibu: $3(5p+4)(q−1)$

Zoezi$\PageIndex{54}$

$12ab−6a+10b−5$

Zoezi$\PageIndex{55}$

$4x^2+40x+84$

Jibu: $4(x+3)(x+7)$

Zoezi$\PageIndex{56}$

$5q^2−15q−90$

Zoezi$\PageIndex{57}$

$u^5+u^2$

Jibu: $u^{2}(u+1)(u^2−u+1)$

Zoezi$\PageIndex{58}$

$5n^3+320$

Zoezi$\PageIndex{59}$

$4c^2+20cd+81d^2$

Jibu: mkuu

Zoezi$\PageIndex{60}$

$25x^2+35xy+49y^2$

Zoezi$\PageIndex{61}$

$10m^4−6250$

Jibu: $10(m−5)(m+5)(m^2+25)$

Zoezi$\PageIndex{62}$

$3v^4−768$

kila siku Math

Zoezi$\PageIndex{63}$

Watermelon kushuka utamaduni springtime katika Chuo Kikuu cha California San Diego ni Watermelon Drop, ambapo watermelon imeshuka kutoka hadithi ya saba ya Urey Hall.

Binomial$−16t^2+80$ inatoa urefu wa watermelon t sekunde baada ya kushuka. Factor sababu kubwa ya kawaida kutoka binomial hii.
Ikiwa mtunguli unatupwa chini na kasi ya awali 8 miguu kwa pili, urefu wake baada ya sekunde t hutolewa na trinomial$−16t2−8t+80$

Jibu

$−16(t^2−5)$
-8 (2t+5) (t-2)

Zoezi$\PageIndex{64}$

Malenge tone kuanguka utamaduni katika Chuo Kikuu cha California San Diego ni pumpkin Drop, ambapo pumpkin imeshuka kutoka hadithi kumi na moja ya Tioga Hall.

Binomial$−16t^2+128$ inatoa urefu wa malenge t sekunde baada ya kushuka. Factor sababu kubwa ya kawaida kutoka binomial hii.
Ikiwa malenge huponywa chini na kasi ya awali ya miguu 32 kwa pili, urefu wake baada ya sekunde t hutolewa na trinomial$−16t^2−32t+128$

Mazoezi ya kuandika

Zoezi$\PageIndex{65}$

Tofauti ya mraba$y^4−625$ inaweza kuzingatiwa kama$(y^2−25)(y^2+25)$ ilivyoelezwa kabisa. Nini zaidi lazima ifanyike ili kuzingatia kabisa?

Zoezi$\PageIndex{66}$

Ya mbinu zote factoring kufunikwa katika sura hii (GCF, kambi, tengua FOIL, 'ac' njia, bidhaa maalum) ambayo ni rahisi kwa ajili yenu? Ambayo ni ngumu zaidi? Eleza majibu yako.

Self Check

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

$Jedwali hili lina kauli zifuatazo zote kutanguliwa na “Naweza...”. Mstari unasema “kutambua na kutumia njia sahihi ya kuzingatia polynomial kabisa”. Katika nguzo kando ya kauli hizi ni vichwa, “kwa ujasiri”, “kwa msaada fulani”, na “Hakuna-siipati!”.$

b Kwa ujumla, baada ya kuangalia orodha, unafikiri umeandaliwa vizuri kwa sehemu inayofuata? Kwa nini au kwa nini?

Zoezi\(\PageIndex{31}\)

Zoezi\(\PageIndex{32}\)

Zoezi\(\PageIndex{33}\)

Zoezi\(\PageIndex{34}\)

Zoezi\(\PageIndex{35}\)

Zoezi\(\PageIndex{36}\)

Zoezi\(\PageIndex{37}\)

Zoezi\(\PageIndex{38}\)

Zoezi\(\PageIndex{39}\)

Zoezi\(\PageIndex{40}\)

Zoezi\(\PageIndex{41}\)

Zoezi\(\PageIndex{42}\)

Zoezi\(\PageIndex{43}\)

Zoezi\(\PageIndex{44}\)

Zoezi\(\PageIndex{45}\)

Zoezi\(\PageIndex{46}\)

Zoezi\(\PageIndex{47}\)

Zoezi\(\PageIndex{48}\)

Zoezi\(\PageIndex{49}\)

Zoezi\(\PageIndex{50}\)

Zoezi\(\PageIndex{51}\)

Zoezi\(\PageIndex{52}\)

Zoezi\(\PageIndex{53}\)

Zoezi\(\PageIndex{54}\)

Zoezi\(\PageIndex{55}\)

Zoezi\(\PageIndex{56}\)

Zoezi\(\PageIndex{57}\)

Zoezi\(\PageIndex{58}\)

Zoezi\(\PageIndex{59}\)

Zoezi\(\PageIndex{60}\)

Zoezi\(\PageIndex{61}\)

Zoezi\(\PageIndex{62}\)

Zoezi\(\PageIndex{63}\)

Zoezi\(\PageIndex{64}\)

Zoezi\(\PageIndex{65}\)

Zoezi\(\PageIndex{66}\)