Whakaoti i te 10x^2-6+5x-3x^2-12

$$10 x ^ { 2 } - 6 + 5 x - 3 x ^ { 2 } - 12$$

Aromātai

$$\left(7x-9\right)\left(x+2\right)$$

Ngā Upane Otinga

Pahekotia te 10x^{2} me -3x^{2}, ka 7x^{2}.

$$7x^{2}-6+5x-12$$

Tangohia te 12 i te -6, ka -18.

$$7x^{2}-18+5x$$

Tauwehe

$$\left(7x-9\right)\left(x+2\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$7x^{2}+5x-18$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 7x^{2}+ax+bx-18. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=5 ab=7\left(-18\right)=-126$$

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 -126.

$$-1,126 -2,63 -3,42 -6,21 -7,18 -9,14$$

Tātaihia te tapeke mō ia takirua.

$$-1+126=125 -2+63=61 -3+42=39 -6+21=15 -7+18=11 -9+14=5$$

Ko te otinga te takirua ka hoatu i te tapeke 5.

$$a=-9 b=14$$

Tuhia anō te 7x^{2}+5x-18 hei \left(7x^{2}-9x\right)+\left(14x-18\right).

$$\left(7x^{2}-9x\right)+\left(14x-18\right)$$

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

$$x\left(7x-9\right)+2\left(7x-9\right)$$

Whakatauwehea atu te kīanga pātahi 7x-9 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(7x-9\right)\left(x+2\right)$$