Whakaoti i te t^3-7t+6

$$t ^ { 3 } - 7 t + 6$$

Tauwehe

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

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

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

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

$$a+b=-3 ab=1\times 2=2$$

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.

$$a=-2 b=-1$$

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

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

Tauwehea te t i te tuatahi me te -1 i te rōpū tuarua.

$$t\left(t-2\right)-\left(t-2\right)$$

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

$$\left(t-2\right)\left(t-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

$$t^{3}-7t+6$$