Whakaoti i te 10x^4-55x^3+70x^2

$$10 x ^ { 4 } - 55 x ^ { 3 } + 70 x ^ { 2 }$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 5.

$$5\left(2x^{4}-11x^{3}+14x^{2}\right)$$

Whakaarohia te 2x^{4}-11x^{3}+14x^{2}. Tauwehea te x^{2}.

$$x^{2}\left(2x^{2}-11x+14\right)$$

Whakaarohia te 2x^{2}-11x+14. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2x^{2}+ax+bx+14. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=2\times 14=28$$

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 28.

$$-1,-28 -2,-14 -4,-7$$

Tātaihia te tapeke mō ia takirua.

$$-1-28=-29 -2-14=-16 -4-7=-11$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-7 b=-4$$

Tuhia anō te 2x^{2}-11x+14 hei \left(2x^{2}-7x\right)+\left(-4x+14\right).

$$\left(2x^{2}-7x\right)+\left(-4x+14\right)$$

Tauwehea te x i te tuatahi me te -2 i te rōpū tuarua.

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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