Whakaoti i te w^5-13w^4+42w^3

$$w ^ { 5 } - 13 w ^ { 4 } + 42 w ^ { 3 }$$

Tauwehe

$$\left(w-7\right)\left(w-6\right)w^{3}$$

Ngā Upane Otinga

Tauwehea te w^{3}.

$$w^{3}\left(w^{2}-13w+42\right)$$

Whakaarohia te w^{2}-13w+42. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei w^{2}+aw+bw+42. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-13 ab=1\times 42=42$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōraro te a+b, he tōraro hoki a a me b. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 42.

$$-1,-42 -2,-21 -3,-14 -6,-7$$

Tātaihia te tapeke mō ia takirua.

$$-1-42=-43 -2-21=-23 -3-14=-17 -6-7=-13$$

Ko te otinga te takirua ka hoatu i te tapeke -13.

$$a=-7 b=-6$$

Tuhia anō te w^{2}-13w+42 hei \left(w^{2}-7w\right)+\left(-6w+42\right).

$$\left(w^{2}-7w\right)+\left(-6w+42\right)$$

Tauwehea te w i te tuatahi me te -6 i te rōpū tuarua.

$$w\left(w-7\right)-6\left(w-7\right)$$

Whakatauwehea atu te kīanga pātahi w-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(w-7\right)\left(w-6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$w^{3}\left(w-7\right)\left(w-6\right)$$

Aromātai

$$\left(w-7\right)\left(w-6\right)w^{3}$$