Whakaoti i te x^3+5x^2+3x-9

$${ x }^{ 3 } +5 { x }^{ 2 } +3x-9$$

Tauwehe

$$\left(x-1\right)\left(x+3\right)^{2}$$

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 -9, ā, ka wehea e q te whakarea arahanga 1. Ko tetahi pūtake pērā ko -3. Tauwehea te pūrau mā te whakawehe mā te x+3.

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

Whakaarohia te x^{2}+2x-3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\left(-3\right)=-3$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=3$$

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

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

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

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

Whakatauwehea atu te kīanga pātahi x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(x-1\right)\left(x+3\right)^{2}$$

Aromātai

$$\left(x-1\right)\left(x+3\right)^{2}$$