Whakaoti i te 15x^3+25x^2-10x

$$15 x ^ { 3 } + 25 x ^ { 2 } - 10 x$$

Tauwehe

$$5x\left(3x-1\right)\left(x+2\right)$$

Ngā Upane Otinga

Tauwehea te 5.

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

Whakaarohia te 3x^{3}+5x^{2}-2x. Tauwehea te x.

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

Whakaarohia te 3x^{2}+5x-2. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=3\left(-2\right)=-6$$

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 5.

$$a=-1 b=6$$

Tuhia anō te 3x^{2}+5x-2 hei \left(3x^{2}-x\right)+\left(6x-2\right).

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

Tauwehea te x i te tuatahi me te 2 i te rōpū tuarua.

$$x\left(3x-1\right)+2\left(3x-1\right)$$

Whakatauwehea atu te kīanga pātahi 3x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3x-1\right)\left(x+2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$5x\left(3x-1\right)\left(x+2\right)$$

Aromātai

$$5x\left(3x-1\right)\left(x+2\right)$$