Whakaoti i te r^4+9r^3+14r^2

$$r ^ { 4 } + 9 r ^ { 3 } + 14 r ^ { 2 }$$

Tauwehe

$$\left(r+2\right)\left(r+7\right)r^{2}$$

Ngā Upane Otinga

Tauwehea te r^{2}.

$$r^{2}\left(r^{2}+9r+14\right)$$

Whakaarohia te r^{2}+9r+14. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei r^{2}+ar+br+14. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=9 ab=1\times 14=14$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 14.

$$1,14 2,7$$

Tātaihia te tapeke mō ia takirua.

$$1+14=15 2+7=9$$

Ko te otinga te takirua ka hoatu i te tapeke 9.

$$a=2 b=7$$

Tuhia anō te r^{2}+9r+14 hei \left(r^{2}+2r\right)+\left(7r+14\right).

$$\left(r^{2}+2r\right)+\left(7r+14\right)$$

Tauwehea te r i te tuatahi me te 7 i te rōpū tuarua.

$$r\left(r+2\right)+7\left(r+2\right)$$

Whakatauwehea atu te kīanga pātahi r+2 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(r+2\right)\left(r+7\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$r^{2}\left(r+2\right)\left(r+7\right)$$

Aromātai

$$\left(r+2\right)\left(r+7\right)r^{2}$$