Whakaoti i te f(x)=4x^3-16x^2-23x+15

$$f ( x ) = 4 x ^ { 3 } - 16 x ^ { 2 } - 23 x + 15$$

Tauwehe

$$\left(x-5\right)\left(2x-1\right)\left(2x+3\right)$$

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 4. Ko tetahi pūtake pērā ko -\frac{3}{2}. Tauwehea te pūrau mā te whakawehe mā te 2x+3.

$$\left(2x+3\right)\left(2x^{2}-11x+5\right)$$

Whakaarohia te 2x^{2}-11x+5. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2x^{2}+ax+bx+5. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-11 ab=2\times 5=10$$

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 10.

$$-1,-10 -2,-5$$

Tātaihia te tapeke mō ia takirua.

$$-1-10=-11 -2-5=-7$$

Ko te otinga te takirua ka hoatu i te tapeke -11.

$$a=-10 b=-1$$

Tuhia anō te 2x^{2}-11x+5 hei \left(2x^{2}-10x\right)+\left(-x+5\right).

$$\left(2x^{2}-10x\right)+\left(-x+5\right)$$

Tauwehea te 2x i te tuatahi me te -1 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi x-5 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-5\right)\left(2x-1\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(x-5\right)\left(2x-1\right)\left(2x+3\right)$$

Aromātai

$$\left(x-5\right)\left(2x-1\right)\left(2x+3\right)$$