Whakaoti i te C(t)=3t^4+18t^3+15t^2

$$C ( t ) = 3 t ^ { 4 } + 18 t ^ { 3 } + 15 t ^ { 2 }$$

Tauwehe

$$3\left(t+1\right)\left(t+5\right)t^{2}$$

Ngā Upane Otinga

Tauwehea te 3.

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

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

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

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

$$a+b=6 ab=1\times 5=5$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=5$$

Tuhia anō te t^{2}+6t+5 hei \left(t^{2}+t\right)+\left(5t+5\right).

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

Tauwehea te t i te tuatahi me te 5 i te rōpū tuarua.

$$t\left(t+1\right)+5\left(t+1\right)$$

Whakatauwehea atu te kīanga pātahi t+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(t+1\right)\left(t+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3t^{2}\left(t+1\right)\left(t+5\right)$$

Aromātai

$$3\left(t+1\right)\left(t+5\right)t^{2}$$