Whakaoti i te 3p^4+28p^3+60p^2

$$3 p ^ { 4 } + 28 p ^ { 3 } + 60 p ^ { 2 }$$

Tauwehe

$$\left(p+6\right)\left(3p+10\right)p^{2}$$

Ngā Upane Otinga

Tauwehea te p^{2}.

$$p^{2}\left(3p^{2}+28p+60\right)$$

Whakaarohia te 3p^{2}+28p+60. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3p^{2}+ap+bp+60. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=28 ab=3\times 60=180$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 180.

$$1,180 2,90 3,60 4,45 5,36 6,30 9,20 10,18 12,15$$

Tātaihia te tapeke mō ia takirua.

$$1+180=181 2+90=92 3+60=63 4+45=49 5+36=41 6+30=36 9+20=29 10+18=28 12+15=27$$

Ko te otinga te takirua ka hoatu i te tapeke 28.

$$a=10 b=18$$

Tuhia anō te 3p^{2}+28p+60 hei \left(3p^{2}+10p\right)+\left(18p+60\right).

$$\left(3p^{2}+10p\right)+\left(18p+60\right)$$

Tauwehea te p i te tuatahi me te 6 i te rōpū tuarua.

$$p\left(3p+10\right)+6\left(3p+10\right)$$

Whakatauwehea atu te kīanga pātahi 3p+10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3p+10\right)\left(p+6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$p^{2}\left(3p+10\right)\left(p+6\right)$$

Aromātai

$$\left(p+6\right)\left(3p+10\right)p^{2}$$