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\left(x-4\right)\left(x^{2}-x-2\right)
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 8, ā, ka wehea e q te whakarea arahanga 1. Ko tetahi pūtake pērā ko 4. Tauwehea te pūrau mā te whakawehe mā te x-4.
a+b=-1 ab=1\left(-2\right)=-2
Whakaarohia te x^{2}-x-2. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx-2. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.
a=-2 b=1
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.
\left(x^{2}-2x\right)+\left(x-2\right)
Tuhia anō te x^{2}-x-2 hei \left(x^{2}-2x\right)+\left(x-2\right).
x\left(x-2\right)+x-2
Whakatauwehea atu x i te x^{2}-2x.
\left(x-2\right)\left(x+1\right)
Whakatauwehea atu te kīanga pātahi x-2 mā te whakamahi i te āhuatanga tātai tohatoha.
\left(x-4\right)\left(x-2\right)\left(x+1\right)
Me tuhi anō te kīanga whakatauwehe katoa.