Whakaoti i te P(x)=x^4-5x^3+5x^2+5x-6

$$P ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 5 x ^ { 2 } + 5 x - 6$$

Tauwehe

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

Ngā Upane Otinga

Kia tauwehea ai te kīanga, me whakaoti te whārite ina ōrite ki te 0.

$$x^{4}-5x^{3}+5x^{2}+5x-6=0$$

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 -6, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±6,±3,±2,±1$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$x=1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{4}-5x^{3}+5x^{2}+5x-6 ki te x-1, kia riro ko x^{3}-4x^{2}+x+6. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$x^{3}-4x^{2}+x+6=0$$

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 6, ā, ka wehea e q te whakarea arahanga 1. Whakarārangitia ngā kaitono katoa \frac{p}{q}.

$$±6,±3,±2,±1$$

Kimihia tētahi pūtake pērā mā te whakamātau i ngā uara tau tōpū katoa, e tīmata ana i te mea iti rawa mā te uara pū. Mēnā kāore he pūtake tau tōpū e kitea, whakamātauria ngā hautanga.

$$x=-1$$

Mā te whakatakotoranga Tauwehe, he tauwehe te x-k o te pūrau mō ia pūtake k. Whakawehea te x^{3}-4x^{2}+x+6 ki te x+1, kia riro ko x^{2}-5x+6. Kia tauwehea ai te otinga, me whakaoti te whārite ina ōrite ki te 0.

$$x^{2}-5x+6=0$$

Ka taea ngā whārite katoa o te momo ax^{2}+bx+c=0 te whakaoti mā te ture pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Whakakapia te 1 mō te a, te -5 mō te b, me te 6 mō te c i te ture pūrua.

$$x=\frac{-\left(-5\right)±\sqrt{\left(-5\right)^{2}-4\times 1\times 6}}{2}$$

Mahia ngā tātaitai.

$$x=\frac{5±1}{2}$$

Whakaotia te whārite x^{2}-5x+6=0 ina he tōrunga te ±, ina he tōraro te ±.

$$x=2 x=3$$

Me tuhi anō te kīanga whakatauwehe mā ngā pūtake i riro.

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

Aromātai

$$\left(x-3\right)\left(x-2\right)\left(x^{2}-1\right)$$