Whakaoti i te 14x^2-8+3x-5x^2-12

$$14 x ^ { 2 } - 8 + 3 x - 5 x ^ { 2 } - 12$$

Aromātai

$$\left(3x-4\right)\left(3x+5\right)$$

Ngā Upane Otinga

Pahekotia te 14x^{2} me -5x^{2}, ka 9x^{2}.

$$9x^{2}-8+3x-12$$

Tangohia te 12 i te -8, ka -20.

$$9x^{2}-20+3x$$

Tauwehe

$$\left(3x-4\right)\left(3x+5\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$9x^{2}+3x-20$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 9x^{2}+ax+bx-20. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=9\left(-20\right)=-180$$

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 -180.

$$-1,180 -2,90 -3,60 -4,45 -5,36 -6,30 -9,20 -10,18 -12,15$$

Tātaihia te tapeke mō ia takirua.

$$-1+180=179 -2+90=88 -3+60=57 -4+45=41 -5+36=31 -6+30=24 -9+20=11 -10+18=8 -12+15=3$$

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

$$a=-12 b=15$$

Tuhia anō te 9x^{2}+3x-20 hei \left(9x^{2}-12x\right)+\left(15x-20\right).

$$\left(9x^{2}-12x\right)+\left(15x-20\right)$$

Tauwehea te 3x i te tuatahi me te 5 i te rōpū tuarua.

$$3x\left(3x-4\right)+5\left(3x-4\right)$$

Whakatauwehea atu te kīanga pātahi 3x-4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3x-4\right)\left(3x+5\right)$$