Whakaoti i te g(x)=x^3-31x-30

$$g ( x ) = x ^ { 3 } - 31 x - 30$$

Tauwehe

$$\left(x-6\right)\left(x+1\right)\left(x+5\right)$$

Ngā Upane Otinga

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 -30, ā, ka wehea e q te whakarea arahanga 1. Ko tetahi pūtake pērā ko 6. Tauwehea te pūrau mā te whakawehe mā te x-6.

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

Whakaarohia te x^{2}+6x+5. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=6 ab=1\times 5=5$$

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. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=5$$

Tuhia anō te x^{2}+6x+5 hei \left(x^{2}+x\right)+\left(5x+5\right).

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

Tauwehea te x i te tuatahi me te 5 i te rōpū tuarua.

$$x\left(x+1\right)+5\left(x+1\right)$$

Whakatauwehea atu te kīanga pātahi x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x+1\right)\left(x+5\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(x-6\right)\left(x+1\right)\left(x+5\right)$$

Aromātai

$$x^{3}-31x-30$$