Whakaoti i te x^4-2x^3-35x^2

$$x ^ { 4 } - 2 x ^ { 3 } - 35 x ^ { 2 }$$

Tauwehe

$$\left(x-7\right)\left(x+5\right)x^{2}$$

Ngā Upane Otinga

Tauwehea te x^{2}.

$$x^{2}\left(x^{2}-2x-35\right)$$

Whakaarohia te x^{2}-2x-35. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-2 ab=1\left(-35\right)=-35$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -35.

$$1,-35 5,-7$$

Tātaihia te tapeke mō ia takirua.

$$1-35=-34 5-7=-2$$

Ko te otinga te takirua ka hoatu i te tapeke -2.

$$a=-7 b=5$$

Tuhia anō te x^{2}-2x-35 hei \left(x^{2}-7x\right)+\left(5x-35\right).

$$\left(x^{2}-7x\right)+\left(5x-35\right)$$

Tauwehea te x i te tuatahi me te 5 i te rōpū tuarua.

$$x\left(x-7\right)+5\left(x-7\right)$$

Whakatauwehea atu te kīanga pātahi x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-7\right)\left(x+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x^{2}\left(x-7\right)\left(x+5\right)$$

Aromātai

$$\left(x-7\right)\left(x+5\right)x^{2}$$