Whakaoti i te x^3+7x^2-18x

$$x ^ { 3 } + 7 x ^ { 2 } - 18 x$$

Tauwehe

$$x\left(x-2\right)\left(x+9\right)$$

Ngā Upane Otinga

Tauwehea te x.

$$x\left(x^{2}+7x-18\right)$$

Whakaarohia te x^{2}+7x-18. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=7 ab=1\left(-18\right)=-18$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -18.

$$-1,18 -2,9 -3,6$$

Tātaihia te tapeke mō ia takirua.

$$-1+18=17 -2+9=7 -3+6=3$$

Ko te otinga te takirua ka hoatu i te tapeke 7.

$$a=-2 b=9$$

Tuhia anō te x^{2}+7x-18 hei \left(x^{2}-2x\right)+\left(9x-18\right).

$$\left(x^{2}-2x\right)+\left(9x-18\right)$$

Tauwehea te x i te tuatahi me te 9 i te rōpū tuarua.

$$x\left(x-2\right)+9\left(x-2\right)$$

Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-2\right)\left(x+9\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x\left(x-2\right)\left(x+9\right)$$

Aromātai

$$x\left(x-2\right)\left(x+9\right)$$