Whakaoti i te x^3+3x^2-6x-8

$$x ^ { 3 } + 3 x ^ { 2 } - 6 x - 8$$

Tauwehe

$$\left(x-2\right)\left(x+1\right)\left(x+4\right)$$

Ngā Upane Otinga

Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau -8, ā, ka wehea e q te whakarea arahanga 1. Ko tetahi pūtake pērā ko -4. Tauwehea te pūrau mā te whakawehe mā te x+4.

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

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

$$a+b=-1 ab=1\left(-2\right)=-2$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-2 b=1$$

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

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

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

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

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

$$\left(x-2\right)\left(x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(x-2\right)\left(x+1\right)\left(x+4\right)$$

Aromātai

$$\left(x-2\right)\left(x+1\right)\left(x+4\right)$$