Whakaoti i te 6x^4+24x^3-360x^2

$$6 x ^ { 4 } + 24 x ^ { 3 } - 360 x ^ { 2 }$$

Tauwehe

$$6\left(x-6\right)\left(x+10\right)x^{2}$$

Ngā Upane Otinga

Tauwehea te 6.

$$6\left(x^{4}+4x^{3}-60x^{2}\right)$$

Whakaarohia te x^{4}+4x^{3}-60x^{2}. Tauwehea te x^{2}.

$$x^{2}\left(x^{2}+4x-60\right)$$

Whakaarohia te x^{2}+4x-60. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-60. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=4 ab=1\left(-60\right)=-60$$

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 -60.

$$-1,60 -2,30 -3,20 -4,15 -5,12 -6,10$$

Tātaihia te tapeke mō ia takirua.

$$-1+60=59 -2+30=28 -3+20=17 -4+15=11 -5+12=7 -6+10=4$$

Ko te otinga te takirua ka hoatu i te tapeke 4.

$$a=-6 b=10$$

Tuhia anō te x^{2}+4x-60 hei \left(x^{2}-6x\right)+\left(10x-60\right).

$$\left(x^{2}-6x\right)+\left(10x-60\right)$$

Tauwehea te x i te tuatahi me te 10 i te rōpū tuarua.

$$x\left(x-6\right)+10\left(x-6\right)$$

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-6\right)\left(x+10\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6x^{2}\left(x-6\right)\left(x+10\right)$$

Aromātai

$$6\left(x-6\right)\left(x+10\right)x^{2}$$