Whakaoti i te a^5-7a^4+12a^3

$$a ^ { 5 } - 7 a ^ { 4 } + 12 a ^ { 3 }$$

Tauwehe

$$\left(a-4\right)\left(a-3\right)a^{3}$$

Ngā Upane Otinga

Tauwehea te a^{3}.

$$a^{3}\left(a^{2}-7a+12\right)$$

Whakaarohia te a^{2}-7a+12. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei a^{2}+pa+qa+12. Hei kimi p me q, whakaritea tētahi pūnaha kia whakaoti.

$$p+q=-7 pq=1\times 12=12$$

I te mea kua tōrunga te pq, he ōrite te tohu o p me q. I te mea kua tōraro te p+q, he tōraro hoki a p me q. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 12.

$$-1,-12 -2,-6 -3,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

Ko te otinga te takirua ka hoatu i te tapeke -7.

$$p=-4 q=-3$$

Tuhia anō te a^{2}-7a+12 hei \left(a^{2}-4a\right)+\left(-3a+12\right).

$$\left(a^{2}-4a\right)+\left(-3a+12\right)$$

Tauwehea te a i te tuatahi me te -3 i te rōpū tuarua.

$$a\left(a-4\right)-3\left(a-4\right)$$

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

$$\left(a-4\right)\left(a-3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$a^{3}\left(a-4\right)\left(a-3\right)$$

Aromātai

$$\left(a-4\right)\left(a-3\right)a^{3}$$