Whakaoti i te 6x^6-21x^5+15x^4

$$6 x ^ { 6 } - 21 x ^ { 5 } + 15 x ^ { 4 }$$

Tauwehe

$$3\left(x-1\right)\left(2x-5\right)x^{4}$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(2x^{6}-7x^{5}+5x^{4}\right)$$

Whakaarohia te 2x^{6}-7x^{5}+5x^{4}. Tauwehea te x^{4}.

$$x^{4}\left(2x^{2}-7x+5\right)$$

Whakaarohia te 2x^{2}-7x+5. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2x^{2}+ax+bx+5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-7 ab=2\times 5=10$$

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 10.

$$-1,-10 -2,-5$$

Tātaihia te tapeke mō ia takirua.

$$-1-10=-11 -2-5=-7$$

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

$$a=-5 b=-2$$

Tuhia anō te 2x^{2}-7x+5 hei \left(2x^{2}-5x\right)+\left(-2x+5\right).

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

Tauwehea te x i te tuatahi me te -1 i te rōpū tuarua.

$$x\left(2x-5\right)-\left(2x-5\right)$$

Whakatauwehea atu te kīanga pātahi 2x-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2x-5\right)\left(x-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3x^{4}\left(2x-5\right)\left(x-1\right)$$

Aromātai

$$3\left(x-1\right)\left(2x-5\right)x^{4}$$