Whakaoti i te 3x^3-5x^2-11x-3

$$3 x ^ { 3 } - 5 x ^ { 2 } - 11 x - 3$$

Tauwehe

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

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

$$\left(x+1\right)\left(3x^{2}-8x-3\right)$$

Whakaarohia te 3x^{2}-8x-3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-8 ab=3\left(-3\right)=-9$$

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 -9.

$$1,-9 3,-3$$

Tātaihia te tapeke mō ia takirua.

$$1-9=-8 3-3=0$$

Ko te otinga te takirua ka hoatu i te tapeke -8.

$$a=-9 b=1$$

Tuhia anō te 3x^{2}-8x-3 hei \left(3x^{2}-9x\right)+\left(x-3\right).

$$\left(3x^{2}-9x\right)+\left(x-3\right)$$

Whakatauwehea atu 3x i te 3x^{2}-9x.

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

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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