Whakaoti i te 9t^3-90t^2+144t

$$9 t ^ { 3 } - 90 t ^ { 2 } + 144 t$$

Tauwehe

$$9t\left(t-8\right)\left(t-2\right)$$

Ngā Upane Otinga

Tauwehea te 9.

$$9\left(t^{3}-10t^{2}+16t\right)$$

Whakaarohia te t^{3}-10t^{2}+16t. Tauwehea te t.

$$t\left(t^{2}-10t+16\right)$$

Whakaarohia te t^{2}-10t+16. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei t^{2}+at+bt+16. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-10 ab=1\times 16=16$$

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 16.

$$-1,-16 -2,-8 -4,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-16=-17 -2-8=-10 -4-4=-8$$

Ko te otinga te takirua ka hoatu i te tapeke -10.

$$a=-8 b=-2$$

Tuhia anō te t^{2}-10t+16 hei \left(t^{2}-8t\right)+\left(-2t+16\right).

$$\left(t^{2}-8t\right)+\left(-2t+16\right)$$

Tauwehea te t i te tuatahi me te -2 i te rōpū tuarua.

$$t\left(t-8\right)-2\left(t-8\right)$$

Whakatauwehea atu te kīanga pātahi t-8 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(t-8\right)\left(t-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$9t\left(t-8\right)\left(t-2\right)$$

Aromātai

$$9t\left(t-8\right)\left(t-2\right)$$