Whakaoti i te x^3-x^2-22x+40

$$x ^ { 3 } - x ^ { 2 } - 22 x + 40$$

Tauwehe

$$\left(x-4\right)\left(x-2\right)\left(x+5\right)$$

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 40, ā, ka wehea e q te whakarea arahanga 1. Ko tetahi pūtake pērā ko -5. Tauwehea te pūrau mā te whakawehe mā te x+5.

$$\left(x+5\right)\left(x^{2}-6x+8\right)$$

Whakaarohia te x^{2}-6x+8. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+8. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-6 ab=1\times 8=8$$

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 8.

$$-1,-8 -2,-4$$

Tātaihia te tapeke mō ia takirua.

$$-1-8=-9 -2-4=-6$$

Ko te otinga te takirua ka hoatu i te tapeke -6.

$$a=-4 b=-2$$

Tuhia anō te x^{2}-6x+8 hei \left(x^{2}-4x\right)+\left(-2x+8\right).

$$\left(x^{2}-4x\right)+\left(-2x+8\right)$$

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

$$x\left(x-4\right)-2\left(x-4\right)$$

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

$$\left(x-4\right)\left(x-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(x-4\right)\left(x-2\right)\left(x+5\right)$$

Aromātai

$$\left(x-4\right)\left(x-2\right)\left(x+5\right)$$