Whakaoti i te (-1-3x+4x^2)+(4x-3x^3-1)

$$( - 1 - 3 x + 4 x ^ { 2 } ) + ( 4 x - 3 x ^ { 3 } - 1 )$$

Aromātai

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

Ngā Upane Otinga

Pahekotia te -3x me 4x, ka x.

$$-1+x+4x^{2}-3x^{3}-1$$

Tangohia te 1 i te -1, ka -2.

$$-2+x+4x^{2}-3x^{3}$$

Tauwehe

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

Ngā Upane Otinga

Whakarea ka paheko i ngā kīanga tau ōrite.

$$-3x^{3}+4x^{2}+x-2$$

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 -2, ā, ka wehea e q te whakarea arahanga -3. Ko tetahi pūtake pērā ko -\frac{2}{3}. Tauwehea te pūrau mā te whakawehe mā te 3x+2.

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

Whakaarohia te -x^{2}+2x-1. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei -x^{2}+ax+bx-1. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=-\left(-1\right)=1$$

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.

$$a=1 b=1$$

Tuhia anō te -x^{2}+2x-1 hei \left(-x^{2}+x\right)+\left(x-1\right).

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

Whakatauwehea atu -x i te -x^{2}+x.

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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