Whakaoti i te 12x^3+16x^2-5x-3

$$12 x ^ { 3 } + 16 x ^ { 2 } - 5 x - 3$$

Tauwehe

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

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 -3, ā, ka wehea e q te whakarea arahanga 12. Ko tetahi pūtake pērā ko -\frac{1}{3}. Tauwehea te pūrau mā te whakawehe mā te 3x+1.

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

Whakaarohia te 4x^{2}+4x-3. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 4x^{2}+ax+bx-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=4 ab=4\left(-3\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua -12.

$$-1,12 -2,6 -3,4$$

Tātaihia te tapeke mō ia takirua.

$$-1+12=11 -2+6=4 -3+4=1$$

Ko te otinga te takirua ka hoatu i te tapeke 4.

$$a=-2 b=6$$

Tuhia anō te 4x^{2}+4x-3 hei \left(4x^{2}-2x\right)+\left(6x-3\right).

$$\left(4x^{2}-2x\right)+\left(6x-3\right)$$

Tauwehea te 2x i te tuatahi me te 3 i te rōpū tuarua.

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

Whakatauwehea atu te kīanga pātahi 2x-1 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Aromātai

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