Whakaoti i te -20m^2q-3mq+35q

$$- 20 m ^ { 2 } q - 3 m q + 35 q$$

Tauwehe

$$-q\left(4m-5\right)\left(5m+7\right)$$

Ngā Upane Otinga

Tauwehea te q.

$$q\left(-20m^{2}-3m+35\right)$$

Whakaarohia te -20m^{2}-3m+35. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -20m^{2}+am+bm+35. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-3 ab=-20\times 35=-700$$

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 -700.

$$1,-700 2,-350 4,-175 5,-140 7,-100 10,-70 14,-50 20,-35 25,-28$$

Tātaihia te tapeke mō ia takirua.

$$1-700=-699 2-350=-348 4-175=-171 5-140=-135 7-100=-93 10-70=-60 14-50=-36 20-35=-15 25-28=-3$$

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

$$a=25 b=-28$$

Tuhia anō te -20m^{2}-3m+35 hei \left(-20m^{2}+25m\right)+\left(-28m+35\right).

$$\left(-20m^{2}+25m\right)+\left(-28m+35\right)$$

Tauwehea te -5m i te tuatahi me te -7 i te rōpū tuarua.

$$-5m\left(4m-5\right)-7\left(4m-5\right)$$

Whakatauwehea atu te kīanga pātahi 4m-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(4m-5\right)\left(-5m-7\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$q\left(4m-5\right)\left(-5m-7\right)$$

Aromātai

$$-q\left(4m-5\right)\left(5m+7\right)$$