Whakaoti i te 12a^3+22a^2-70a

$$12 a ^ { 3 } + 22 a ^ { 2 } - 70 a$$

Tauwehe

$$2a\left(3a-5\right)\left(2a+7\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(6a^{3}+11a^{2}-35a\right)$$

Whakaarohia te 6a^{3}+11a^{2}-35a. Tauwehea te a.

$$a\left(6a^{2}+11a-35\right)$$

Whakaarohia te 6a^{2}+11a-35. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6a^{2}+pa+qa-35. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=11 pq=6\left(-35\right)=-210$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōrunga te p+q, 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 -210.

$$-1,210 -2,105 -3,70 -5,42 -6,35 -7,30 -10,21 -14,15$$

Tātaihia te tapeke mō ia takirua.

$$-1+210=209 -2+105=103 -3+70=67 -5+42=37 -6+35=29 -7+30=23 -10+21=11 -14+15=1$$

Ko te otinga te takirua ka hoatu i te tapeke 11.

$$p=-10 q=21$$

Tuhia anō te 6a^{2}+11a-35 hei \left(6a^{2}-10a\right)+\left(21a-35\right).

$$\left(6a^{2}-10a\right)+\left(21a-35\right)$$

Tauwehea te 2a i te tuatahi me te 7 i te rōpū tuarua.

$$2a\left(3a-5\right)+7\left(3a-5\right)$$

Whakatauwehea atu te kīanga pātahi 3a-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3a-5\right)\left(2a+7\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2a\left(3a-5\right)\left(2a+7\right)$$

Aromātai

$$2a\left(3a-5\right)\left(2a+7\right)$$