Whakaoti i te x^3+6x^2-7x

$${ x }^{ 3 } +6 { x }^{ 2 } -7x$$

Tauwehe

$$x\left(x-1\right)\left(x+7\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(x^{2}+6x-7\right)$$

Whakaarohia te x^{2}+6x-7. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-7. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\left(-7\right)=-7$$

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.

$$a=-1 b=7$$

Tuhia anō te x^{2}+6x-7 hei \left(x^{2}-x\right)+\left(7x-7\right).

$$\left(x^{2}-x\right)+\left(7x-7\right)$$

Tauwehea te x i te tuatahi me te 7 i te rōpū tuarua.

$$x\left(x-1\right)+7\left(x-1\right)$$

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

$$\left(x-1\right)\left(x+7\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x\left(x-1\right)\left(x+7\right)$$

Aromātai

$$x\left(x-1\right)\left(x+7\right)$$