Whakaoti i te x^3+8x^2+17x+10

$$x ^ { 3 } + 8 x ^ { 2 } + 17 x + 10$$

Tauwehe

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

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 10, 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.

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

Whakaarohia te x^{2}+3x+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.

$$a+b=3 ab=1\times 2=2$$

I te mea kua tōrunga te ab, he ōrite te tohu o a me b. I te mea kua tōrunga te a+b, he tōrunga hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=1 b=2$$

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

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

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

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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