Whakaoti i te abx^2-5abx-24ab

$$a b x ^ { 2 } - 5 a b x - 24 a b$$

Tauwehe

$$ab\left(x-8\right)\left(x+3\right)$$

Ngā Upane Otinga

Tauwehea te ab.

$$ab\left(x^{2}-5x-24\right)$$

Whakaarohia te x^{2}-5x-24. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+px+qx-24. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=-5 pq=1\left(-24\right)=-24$$

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 -24.

$$1,-24 2,-12 3,-8 4,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-24=-23 2-12=-10 3-8=-5 4-6=-2$$

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

$$p=-8 q=3$$

Tuhia anō te x^{2}-5x-24 hei \left(x^{2}-8x\right)+\left(3x-24\right).

$$\left(x^{2}-8x\right)+\left(3x-24\right)$$

Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.

$$x\left(x-8\right)+3\left(x-8\right)$$

Whakatauwehea atu te kīanga pātahi x-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-8\right)\left(x+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$ab\left(x-8\right)\left(x+3\right)$$

Aromātai

$$ab\left(x-8\right)\left(x+3\right)$$