Whakaoti i te 24x^3+18x^2-6x

$$24 x ^ { 3 } + 18 x ^ { 2 } - 6 x$$

Tauwehe

$$6x\left(4x-1\right)\left(x+1\right)$$

Ngā Upane Otinga

Tauwehea te 6.

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

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

$$x\left(4x^{2}+3x-1\right)$$

Whakaarohia te 4x^{2}+3x-1. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 4x^{2}+ax+bx-1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=4\left(-1\right)=-4$$

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 -4.

$$-1,4 -2,2$$

Tātaihia te tapeke mō ia takirua.

$$-1+4=3 -2+2=0$$

Ko te otinga te takirua ka hoatu i te tapeke 3.

$$a=-1 b=4$$

Tuhia anō te 4x^{2}+3x-1 hei \left(4x^{2}-x\right)+\left(4x-1\right).

$$\left(4x^{2}-x\right)+\left(4x-1\right)$$

Whakatauwehea atu x i te 4x^{2}-x.

$$x\left(4x-1\right)+4x-1$$

Whakatauwehea atu te kīanga pātahi 4x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(4x-1\right)\left(x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$6x\left(4x-1\right)\left(x+1\right)$$

Aromātai

$$6x\left(4x-1\right)\left(x+1\right)$$