Whakaoti i te 3x^3+31x^2+82x+24

$$3 x ^ { 3 } + 31 x ^ { 2 } + 82 x + 24$$

Tauwehe

$$\left(x+4\right)\left(x+6\right)\left(3x+1\right)$$

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 24, ā, ka wehea e q te whakarea arahanga 3. Ko tetahi pūtake pērā ko -4. Tauwehea te pūrau mā te whakawehe mā te x+4.

$$\left(x+4\right)\left(3x^{2}+19x+6\right)$$

Whakaarohia te 3x^{2}+19x+6. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 3x^{2}+ax+bx+6. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=19 ab=3\times 6=18$$

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. Whakarārangitia ngā tau tōpū takirua pērā katoa ka hoatu i te hua 18.

$$1,18 2,9 3,6$$

Tātaihia te tapeke mō ia takirua.

$$1+18=19 2+9=11 3+6=9$$

Ko te otinga te takirua ka hoatu i te tapeke 19.

$$a=1 b=18$$

Tuhia anō te 3x^{2}+19x+6 hei \left(3x^{2}+x\right)+\left(18x+6\right).

$$\left(3x^{2}+x\right)+\left(18x+6\right)$$

Tauwehea te x i te tuatahi me te 6 i te rōpū tuarua.

$$x\left(3x+1\right)+6\left(3x+1\right)$$

Whakatauwehea atu te kīanga pātahi 3x+1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(3x+1\right)\left(x+6\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$\left(3x+1\right)\left(x+4\right)\left(x+6\right)$$

Aromātai

$$\left(x+4\right)\left(x+6\right)\left(3x+1\right)$$