Whakaoti i te f(x)=x^4+x^3-6x^2

$$f ( x ) = x ^ { 4 } + x ^ { 3 } - 6 x ^ { 2 }$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te x^{2}.

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

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

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

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 -6.

$$-1,6 -2,3$$

Tātaihia te tapeke mō ia takirua.

$$-1+6=5 -2+3=1$$

Ko te otinga te takirua ka hoatu i te tapeke 1.

$$a=-2 b=3$$

Tuhia anō te x^{2}+x-6 hei \left(x^{2}-2x\right)+\left(3x-6\right).

$$\left(x^{2}-2x\right)+\left(3x-6\right)$$

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

$$x\left(x-2\right)+3\left(x-2\right)$$

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

$$\left(x-2\right)\left(x+3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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