Whakaoti i te x^3-15x^2+56x-60

$$x ^ { 3 } - 15 x ^ { 2 } + 56 x - 60$$

Tauwehe

$$\left(x-10\right)\left(x-3\right)\left(x-2\right)$$

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 -60, ā, ka wehea e q te whakarea arahanga 1. Ko tetahi pūtake pērā ko 10. Tauwehea te pūrau mā te whakawehe mā te x-10.

$$\left(x-10\right)\left(x^{2}-5x+6\right)$$

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

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

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 6.

$$-1,-6 -2,-3$$

Tātaihia te tapeke mō ia takirua.

$$-1-6=-7 -2-3=-5$$

Ko te otinga te takirua ka hoatu i te tapeke -5.

$$a=-3 b=-2$$

Tuhia anō te x^{2}-5x+6 hei \left(x^{2}-3x\right)+\left(-2x+6\right).

$$\left(x^{2}-3x\right)+\left(-2x+6\right)$$

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

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

Whakatauwehea atu te kīanga pātahi x-3 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(x-10\right)\left(x-3\right)\left(x-2\right)$$

Aromātai

$$\left(x-10\right)\left(x-3\right)\left(x-2\right)$$