Whakaoti i te 22x^7-83x^6+21x^5

$$22 x ^ { 7 } - 83 x ^ { 6 } + 21 x ^ { 5 }$$

Tauwehe

$$\left(2x-7\right)\left(11x-3\right)x^{5}$$

Ngā Upane Otinga

Tauwehea te x^{5}.

$$x^{5}\left(22x^{2}-83x+21\right)$$

Whakaarohia te 22x^{2}-83x+21. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 22x^{2}+ax+bx+21. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-83 ab=22\times 21=462$$

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 462.

$$-1,-462 -2,-231 -3,-154 -6,-77 -7,-66 -11,-42 -14,-33 -21,-22$$

Tātaihia te tapeke mō ia takirua.

$$-1-462=-463 -2-231=-233 -3-154=-157 -6-77=-83 -7-66=-73 -11-42=-53 -14-33=-47 -21-22=-43$$

Ko te otinga te takirua ka hoatu i te tapeke -83.

$$a=-77 b=-6$$

Tuhia anō te 22x^{2}-83x+21 hei \left(22x^{2}-77x\right)+\left(-6x+21\right).

$$\left(22x^{2}-77x\right)+\left(-6x+21\right)$$

Tauwehea te 11x i te tuatahi me te -3 i te rōpū tuarua.

$$11x\left(2x-7\right)-3\left(2x-7\right)$$

Whakatauwehea atu te kīanga pātahi 2x-7 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2x-7\right)\left(11x-3\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$x^{5}\left(2x-7\right)\left(11x-3\right)$$

Aromātai

$$\left(2x-7\right)\left(11x-3\right)x^{5}$$