Whakaoti i te x^3-x^2-20x

$$x ^ { 3 } - x ^ { 2 } - 20 x$$

Tauwehe

$$x\left(x-5\right)\left(x+4\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(x^{2}-x-20\right)$$

Whakaarohia te x^{2}-x-20. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-20. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-1 ab=1\left(-20\right)=-20$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, 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 -20.

$$1,-20 2,-10 4,-5$$

Tātaihia te tapeke mō ia takirua.

$$1-20=-19 2-10=-8 4-5=-1$$

Ko te otinga te takirua ka hoatu i te tapeke -1.

$$a=-5 b=4$$

Tuhia anō te x^{2}-x-20 hei \left(x^{2}-5x\right)+\left(4x-20\right).

$$\left(x^{2}-5x\right)+\left(4x-20\right)$$

Tauwehea te x i te tuatahi me te 4 i te rōpū tuarua.

$$x\left(x-5\right)+4\left(x-5\right)$$

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

$$\left(x-5\right)\left(x+4\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x\left(x-5\right)\left(x+4\right)$$

Aromātai

$$x\left(x-5\right)\left(x+4\right)$$