Whakaoti i te 2t^5+4t^4-10t^3-12t^2

$$2 t ^ { 5 } + 4 t ^ { 4 } - 10 t ^ { 3 } - 12 t ^ { 2 }$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(t^{5}+2t^{4}-5t^{3}-6t^{2}\right)$$

Whakaarohia te t^{5}+2t^{4}-5t^{3}-6t^{2}. Tauwehea te t^{2}.

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

Whakaarohia te t^{3}+2t^{2}-5t-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 1. Ko tetahi pūtake pērā ko -3. Tauwehea te pūrau mā te whakawehe mā te t+3.

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

Whakaarohia te t^{2}-t-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.

$$a+b=-1 ab=1\left(-2\right)=-2$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-2 b=1$$

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

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

Whakatauwehea atu t i te t^{2}-2t.

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

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.

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

Aromātai

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