Whakaoti i te 3x^3+6x^2-9x

$$3 x ^ { 3 } + 6 x ^ { 2 } - 9 x$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3.

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

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

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

Whakaarohia te x^{2}+2x-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.

$$a+b=2 ab=1\left(-3\right)=-3$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=3$$

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

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

Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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