Whakaoti i te x^3+4x^2-3x-18

$$x ^ { 3 } + 4 x ^ { 2 } - 3 x - 18$$

Tauwehe

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

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 -18, 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.

$$\left(x+3\right)\left(x^{2}+x-6\right)$$

Whakaarohia te x^{2}+x-6. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=1\left(-6\right)=-6$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -6.

$$-1,6 -2,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+6=5 -2+3=1$$

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

$$a=-2 b=3$$

Tuhia anō te x^{2}+x-6 hei \left(x^{2}-2x\right)+\left(3x-6\right).

$$\left(x^{2}-2x\right)+\left(3x-6\right)$$

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

$$x\left(x-2\right)+3\left(x-2\right)$$

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

$$\left(x-2\right)\left(x+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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