Whakaoti i te f(x)=-x^3+3x^2+13x-15

$$f ( x ) = - x ^ { 3 } + 3 x ^ { 2 } + 13 x - 15$$

Tauwehe

$$\left(1-x\right)\left(x-5\right)\left(x+3\right)$$

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 -15, 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.

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

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

$$a+b=-2 ab=-3=-3$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=-3$$

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

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

Tauwehea te x i te tuatahi me te 3 i te rōpū tuarua.

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(x-5\right)\left(-x+1\right)\left(x+3\right)$$

Aromātai

$$\left(1-x\right)\left(x-5\right)\left(x+3\right)$$