Whakaoti i te 18x^2-15x+48x-40

$$18 x ^ { 2 } - 15 x + 48 x - 40$$

Tauwehe

$$\left(6x-5\right)\left(3x+8\right)$$

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$18x^{2}+33x-40$$

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 18x^{2}+ax+bx-40. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=33 ab=18\left(-40\right)=-720$$

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 -720.

$$-1,720 -2,360 -3,240 -4,180 -5,144 -6,120 -8,90 -9,80 -10,72 -12,60 -15,48 -16,45 -18,40 -20,36 -24,30$$

Tātaihia te tapeke mō ia takirua.

$$-1+720=719 -2+360=358 -3+240=237 -4+180=176 -5+144=139 -6+120=114 -8+90=82 -9+80=71 -10+72=62 -12+60=48 -15+48=33 -16+45=29 -18+40=22 -20+36=16 -24+30=6$$

Ko te otinga te takirua ka hoatu i te tapeke 33.

$$a=-15 b=48$$

Tuhia anō te 18x^{2}+33x-40 hei \left(18x^{2}-15x\right)+\left(48x-40\right).

$$\left(18x^{2}-15x\right)+\left(48x-40\right)$$

Tauwehea te 3x i te tuatahi me te 8 i te rōpū tuarua.

$$3x\left(6x-5\right)+8\left(6x-5\right)$$

Whakatauwehea atu te kīanga pātahi 6x-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(6x-5\right)\left(3x+8\right)$$

Aromātai

$$\left(6x-5\right)\left(3x+8\right)$$

Ngā Upane Otinga

Pahekotia te -15x me 48x, ka 33x.

$$18x^{2}+33x-40$$