Whakaoti i te ax^2+4ax-12a

$$a x ^ { 2 } + 4 a x - 12 a$$

Tauwehe

$$a\left(x-2\right)\left(x+6\right)$$

Ngā Upane Otinga

Tauwehea te a.

$$a\left(x^{2}+4x-12\right)$$

Whakaarohia te x^{2}+4x-12. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+px+qx-12. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=4 pq=1\left(-12\right)=-12$$

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 -12.

$$-1,12 -2,6 -3,4$$

Tātaihia te tapeke mō ia takirua.

$$-1+12=11 -2+6=4 -3+4=1$$

Ko te otinga te takirua ka hoatu i te tapeke 4.

$$p=-2 q=6$$

Tuhia anō te x^{2}+4x-12 hei \left(x^{2}-2x\right)+\left(6x-12\right).

$$\left(x^{2}-2x\right)+\left(6x-12\right)$$

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

$$x\left(x-2\right)+6\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(x+6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$a\left(x-2\right)\left(x+6\right)$$

Aromātai

$$a\left(x-2\right)\left(x+6\right)$$