Whakaoti i te 2p^5+10p^4-12p^3

$$2 p ^ { 5 } + 10 p ^ { 4 } - 12 p ^ { 3 }$$

Tauwehe

$$2\left(p-1\right)\left(p+6\right)p^{3}$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(p^{5}+5p^{4}-6p^{3}\right)$$

Whakaarohia te p^{5}+5p^{4}-6p^{3}. Tauwehea te p^{3}.

$$p^{3}\left(p^{2}+5p-6\right)$$

Whakaarohia te p^{2}+5p-6. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei p^{2}+ap+bp-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=1\left(-6\right)=-6$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -6.

$$-1,6 -2,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+6=5 -2+3=1$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=-1 b=6$$

Tuhia anō te p^{2}+5p-6 hei \left(p^{2}-p\right)+\left(6p-6\right).

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

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

$$p\left(p-1\right)+6\left(p-1\right)$$

Whakatauwehea atu te kīanga pātahi p-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(p-1\right)\left(p+6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2p^{3}\left(p-1\right)\left(p+6\right)$$

Aromātai

$$2\left(p-1\right)\left(p+6\right)p^{3}$$