Whakaoti i te g(x)=6x^3-x^2-5x+2

$$g ( x ) = 6 x ^ { 3 } - x ^ { 2 } - 5 x + 2$$

Tauwehe

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

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 2, 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.

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

Whakaarohia te 6x^{2}-7x+2. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 6x^{2}+ax+bx+2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=6\times 2=12$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.

$$-1,-12 -2,-6 -3,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$a=-4 b=-3$$

Tuhia anō te 6x^{2}-7x+2 hei \left(6x^{2}-4x\right)+\left(-3x+2\right).

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

Tauwehea te 2x i te tuatahi me te -1 i te rōpū tuarua.

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

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

$$\left(3x-2\right)\left(2x-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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