Whakaoti i te 3x^2-12x+6-2x-15x^2

$$3 x ^ { 2 } - 12 x + 6 - 2 x - 15 x ^ { 2 }$$

Aromātai

$$6-14x-12x^{2}$$

Ngā Upane Otinga

Pahekotia te -12x me -2x, ka -14x.

$$3x^{2}-14x+6-15x^{2}$$

Pahekotia te 3x^{2} me -15x^{2}, ka -12x^{2}.

$$-12x^{2}-14x+6$$

Tauwehe

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

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$-12x^{2}-14x+6$$

Tauwehea te 2.

$$2\left(-6x^{2}-7x+3\right)$$

Whakaarohia te -6x^{2}-7x+3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -6x^{2}+ax+bx+3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=-6\times 3=-18$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -18.

$$1,-18 2,-9 3,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-18=-17 2-9=-7 3-6=-3$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$a=2 b=-9$$

Tuhia anō te -6x^{2}-7x+3 hei \left(-6x^{2}+2x\right)+\left(-9x+3\right).

$$\left(-6x^{2}+2x\right)+\left(-9x+3\right)$$

Tauwehea te 2x i te tuatahi me te 3 i te rōpū tuarua.

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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