Whakaoti i te 3x^4-12x^3+9x^2=

$$3 x ^ { 4 } - 12 x ^ { 3 } + 9 x ^ { 2 } =$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3.

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

Whakaarohia te x^{4}-4x^{3}+3x^{2}. Tauwehea te x^{2}.

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

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

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

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

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

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

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

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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