Whakaoti i te -3x^4+3x^3+60x^2

$$- 3 x ^ { 4 } + 3 x ^ { 3 } + 60 x ^ { 2 }$$

Tauwehe

$$-3\left(x-5\right)\left(x+4\right)x^{2}$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(-x^{4}+x^{3}+20x^{2}\right)$$

Whakaarohia te -x^{4}+x^{3}+20x^{2}. Tauwehea te x^{2}.

$$x^{2}\left(-x^{2}+x+20\right)$$

Whakaarohia te -x^{2}+x+20. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx+20. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=1 ab=-20=-20$$

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 -20.

$$-1,20 -2,10 -4,5$$

Tātaihia te tapeke mō ia takirua.

$$-1+20=19 -2+10=8 -4+5=1$$

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

$$a=5 b=-4$$

Tuhia anō te -x^{2}+x+20 hei \left(-x^{2}+5x\right)+\left(-4x+20\right).

$$\left(-x^{2}+5x\right)+\left(-4x+20\right)$$

Tauwehea te -x i te tuatahi me te -4 i te rōpū tuarua.

$$-x\left(x-5\right)-4\left(x-5\right)$$

Whakatauwehea atu te kīanga pātahi x-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-5\right)\left(-x-4\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3x^{2}\left(x-5\right)\left(-x-4\right)$$

Aromātai

$$-3\left(x-5\right)\left(x+4\right)x^{2}$$