Whakaoti i te 3ax^2-9ax-12a=

$$3 a x ^ { 2 } - 9 a x - 12 a =$$

Tauwehe

$$3a\left(x-4\right)\left(x+1\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(ax^{2}-3ax-4a\right)$$

Whakaarohia te ax^{2}-3ax-4a. Tauwehea te a.

$$a\left(x^{2}-3x-4\right)$$

Whakaarohia te x^{2}-3x-4. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+px+qx-4. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=-3 pq=1\left(-4\right)=-4$$

I te mea kua tōraro te pq, he tauaro ngā tohu o p me q. I te mea kua tōraro te p+q, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -4.

$$1,-4 2,-2$$

Tātaihia te tapeke mō ia takirua.

$$1-4=-3 2-2=0$$

Ko te otinga te takirua ka hoatu i te tapeke -3.

$$p=-4 q=1$$

Tuhia anō te x^{2}-3x-4 hei \left(x^{2}-4x\right)+\left(x-4\right).

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

Whakatauwehea atu x i te x^{2}-4x.

$$x\left(x-4\right)+x-4$$

Whakatauwehea atu te kīanga pātahi x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-4\right)\left(x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3a\left(x-4\right)\left(x+1\right)$$

Aromātai

$$3a\left(x-4\right)\left(x+1\right)$$