Whakaoti i te 4x^3-7x-3

$$4 { x }^{ 3 } -7x-3$$

Tauwehe

$$\left(2x-3\right)\left(x+1\right)\left(2x+1\right)$$

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 -3, ā, ka wehea e q te whakarea arahanga 4. Ko tetahi pūtake pērā ko \frac{3}{2}. Tauwehea te pūrau mā te whakawehe mā te 2x-3.

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

Whakaarohia te 2x^{2}+3x+1. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2x^{2}+ax+bx+1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=3 ab=2\times 1=2$$

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.

$$a=1 b=2$$

Tuhia anō te 2x^{2}+3x+1 hei \left(2x^{2}+x\right)+\left(2x+1\right).

$$\left(2x^{2}+x\right)+\left(2x+1\right)$$

Whakatauwehea atu x i te 2x^{2}+x.

$$x\left(2x+1\right)+2x+1$$

Whakatauwehea atu te kīanga pātahi 2x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(2x+1\right)\left(x+1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(2x-3\right)\left(x+1\right)\left(2x+1\right)$$

Aromātai

$$4x^{3}-7x-3$$