Whakaoti i te -60pix^2+480pix+1200pi

$$-60 \pi { x }^{ 2 } +480 \pi x+1200 \pi$$

Tauwehe

$$-60\pi \left(x-10\right)\left(x+2\right)$$

Ngā Upane Otinga

Tauwehea te 60.

$$60\left(-\pi x^{2}+8\pi x+20\pi \right)$$

Whakaarohia te -\pi x^{2}+8\pi x+20\pi . Tauwehea te \pi .

$$\pi \left(-x^{2}+8x+20\right)$$

Whakaarohia te -x^{2}+8x+20. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx+20. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=8 ab=-20=-20$$

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 -20.

$$-1,20 -2,10 -4,5$$

Tātaihia te tapeke mō ia takirua.

$$-1+20=19 -2+10=8 -4+5=1$$

Ko te otinga te takirua ka hoatu i te tapeke 8.

$$a=10 b=-2$$

Tuhia anō te -x^{2}+8x+20 hei \left(-x^{2}+10x\right)+\left(-2x+20\right).

$$\left(-x^{2}+10x\right)+\left(-2x+20\right)$$

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

$$-x\left(x-10\right)-2\left(x-10\right)$$

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

$$\left(x-10\right)\left(-x-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$60\pi \left(x-10\right)\left(-x-2\right)$$

Aromātai

$$-60\pi \left(x-10\right)\left(x+2\right)$$