Whakaoti i te 12x^5-8x^4-27x^3+24x^2+5x-6

$$12 x ^ { 5 } - 8 x ^ { 4 } - 27 x ^ { 3 } + 24 x ^ { 2 } + 5 x - 6$$

Tauwehe

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

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 -6, ā, ka wehea e q te whakarea arahanga 12. Ko tetahi pūtake pērā ko -\frac{1}{2}. Tauwehea te pūrau mā te whakawehe mā te 2x+1.

$$\left(2x+1\right)\left(6x^{4}-7x^{3}-10x^{2}+17x-6\right)$$

Whakaarohia te 6x^{4}-7x^{3}-10x^{2}+17x-6. 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 -6, ā, ka wehea e q te whakarea arahanga 6. Ko tetahi pūtake pērā ko 1. Tauwehea te pūrau mā te whakawehe mā te x-1.

$$\left(x-1\right)\left(6x^{3}-x^{2}-11x+6\right)$$

Whakaarohia te 6x^{3}-x^{2}-11x+6. 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 6, ā, ka wehea e q te whakarea arahanga 6. Ko tetahi pūtake pērā ko 1. Tauwehea te pūrau mā te whakawehe mā te x-1.

$$\left(x-1\right)\left(6x^{2}+5x-6\right)$$

Whakaarohia te 6x^{2}+5x-6. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6x^{2}+ax+bx-6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=6\left(-6\right)=-36$$

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 -36.

$$-1,36 -2,18 -3,12 -4,9 -6,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+36=35 -2+18=16 -3+12=9 -4+9=5 -6+6=0$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=-4 b=9$$

Tuhia anō te 6x^{2}+5x-6 hei \left(6x^{2}-4x\right)+\left(9x-6\right).

$$\left(6x^{2}-4x\right)+\left(9x-6\right)$$

Tauwehea te 2x i te tuatahi me te 3 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi 3x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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