Whakaoti i te 36x^2+210x+392+2x^3

$$36 x ^ { 2 } + 210 x + 392 + 2 x ^ { 3 }$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(18x^{2}+105x+196+x^{3}\right)$$

Whakaarohia te 18x^{2}+105x+196+x^{3}. Tā te Rational Root Theorem, ko ngā pūtake whakahau katoa o tētahi pūrau kei te āhua o \frac{p}{q}, ina wehea e p te kīanga pūmau 196, ā, ka wehea e q te whakarea arahanga 1. Ko tetahi pūtake pērā ko -7. Tauwehea te pūrau mā te whakawehe mā te x+7.

$$\left(x+7\right)\left(x^{2}+11x+28\right)$$

Whakaarohia te x^{2}+11x+28. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+28. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=11 ab=1\times 28=28$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga 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.

$$a=4 b=7$$

Tuhia anō te x^{2}+11x+28 hei \left(x^{2}+4x\right)+\left(7x+28\right).

$$\left(x^{2}+4x\right)+\left(7x+28\right)$$

Tauwehea te x i te tuatahi me te 7 i te rōpū tuarua.

$$x\left(x+4\right)+7\left(x+4\right)$$

Whakatauwehea atu te kīanga pātahi x+4 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+4\right)\left(x+7\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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