Whakaoti i te 6x^4-5x^3-2x^2+x=

$$6 x ^ { 4 } - 5 x ^ { 3 } - 2 x ^ { 2 } + x =$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te x.

$$x\left(6x^{3}-5x^{2}-2x+1\right)$$

Whakaarohia te 6x^{3}-5x^{2}-2x+1. 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 1, ā, ka wehea e q te whakarea arahanga 6. Ko tetahi pūtake pērā ko -\frac{1}{2}. Tauwehea te pūrau mā te whakawehe mā te 2x+1.

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

Whakaarohia te 3x^{2}-4x+1. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3x^{2}+ax+bx+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-4 ab=3\times 1=3$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-3 b=-1$$

Tuhia anō te 3x^{2}-4x+1 hei \left(3x^{2}-3x\right)+\left(-x+1\right).

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

Tauwehea te 3x i te tuatahi me te -1 i te rōpū tuarua.

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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