Whakaoti i te 4q^3-20q^2-200q

$$4 q ^ { 3 } - 20 q ^ { 2 } - 200 q$$

Tauwehe

$$4q\left(q-10\right)\left(q+5\right)$$

Ngā Upane Otinga

Tauwehea te 4.

$$4\left(q^{3}-5q^{2}-50q\right)$$

Whakaarohia te q^{3}-5q^{2}-50q. Tauwehea te q.

$$q\left(q^{2}-5q-50\right)$$

Whakaarohia te q^{2}-5q-50. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei q^{2}+aq+bq-50. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-5 ab=1\left(-50\right)=-50$$

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 -50.

$$1,-50 2,-25 5,-10$$

Tātaihia te tapeke mō ia takirua.

$$1-50=-49 2-25=-23 5-10=-5$$

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

$$a=-10 b=5$$

Tuhia anō te q^{2}-5q-50 hei \left(q^{2}-10q\right)+\left(5q-50\right).

$$\left(q^{2}-10q\right)+\left(5q-50\right)$$

Tauwehea te q i te tuatahi me te 5 i te rōpū tuarua.

$$q\left(q-10\right)+5\left(q-10\right)$$

Whakatauwehea atu te kīanga pātahi q-10 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(q-10\right)\left(q+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$4q\left(q-10\right)\left(q+5\right)$$

Aromātai

$$4q\left(q-10\right)\left(q+5\right)$$