Whakaoti i te 3x^2-9x+6

$$3 x ^ { 2 } - 9 x + 6$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 3.

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

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 tōraro te a+b, he tōraro hoki a a me b. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-2 b=-1$$

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

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

Tauwehea te x i te tuatahi me te -1 i te rōpū tuarua.

$$x\left(x-2\right)-\left(x-2\right)$$

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

Ngā Upane e Whakamahi ana i te Tikanga Tātai Pūrua

Ka taea te huamaha pūrua te tauwehe mā te whakamahi i te huringa ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), ina ko x_{1} me x_{2} ngā otinga o te whārite pūrua ax^{2}+bx+c=0.

$$3x^{2}-9x+6=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$x=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}-4\times 3\times 6}}{2\times 3}$$

Pūrua -9.

$$x=\frac{-\left(-9\right)±\sqrt{81-4\times 3\times 6}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-9\right)±\sqrt{81-12\times 6}}{2\times 3}$$

Whakareatia -12 ki te 6.

$$x=\frac{-\left(-9\right)±\sqrt{81-72}}{2\times 3}$$

Tāpiri 81 ki te -72.

$$x=\frac{-\left(-9\right)±\sqrt{9}}{2\times 3}$$

Tuhia te pūtakerua o te 9.

$$x=\frac{-\left(-9\right)±3}{2\times 3}$$

Ko te tauaro o -9 ko 9.

$$x=\frac{9±3}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{9±3}{6}$$

Nā, me whakaoti te whārite x=\frac{9±3}{6} ina he tāpiri te ±. Tāpiri 9 ki te 3.

$$x=\frac{12}{6}$$

Whakawehe 12 ki te 6.

$$x=2$$

Nā, me whakaoti te whārite x=\frac{9±3}{6} ina he tango te ±. Tango 3 mai i 9.

$$x=\frac{6}{6}$$

Whakawehe 6 ki te 6.

$$x=1$$

Tauwehea te kīanga taketake mā te whakamahi i te ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Me whakakapi te 2 mō te x_{1} me te 1 mō te x_{2}.

$$3x^{2}-9x+6=3\left(x-2\right)\left(x-1\right)$$

Aromātai

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