Whakaoti i te 3x^2-24x+36

$$3 x ^ { 2 } - 24 x + 36$$

Tauwehe

$$3\left(x-6\right)\left(x-2\right)$$

Ngā Upane Otinga

Tauwehea te 3.

$$3\left(x^{2}-8x+12\right)$$

Whakaarohia te x^{2}-8x+12. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+12. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-8 ab=1\times 12=12$$

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. 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.

$$-1-12=-13 -2-6=-8 -3-4=-7$$

Ko te otinga te takirua ka hoatu i te tapeke -8.

$$a=-6 b=-2$$

Tuhia anō te x^{2}-8x+12 hei \left(x^{2}-6x\right)+\left(-2x+12\right).

$$\left(x^{2}-6x\right)+\left(-2x+12\right)$$

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

$$x\left(x-6\right)-2\left(x-6\right)$$

Whakatauwehea atu te kīanga pātahi x-6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(x-6\right)\left(x-2\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$3\left(x-6\right)\left(x-2\right)$$

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.

$$3x^{2}-24x+36=0$$

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.

$$x=\frac{-\left(-24\right)±\sqrt{\left(-24\right)^{2}-4\times 3\times 36}}{2\times 3}$$

Pūrua -24.

$$x=\frac{-\left(-24\right)±\sqrt{576-4\times 3\times 36}}{2\times 3}$$

Whakareatia -4 ki te 3.

$$x=\frac{-\left(-24\right)±\sqrt{576-12\times 36}}{2\times 3}$$

Whakareatia -12 ki te 36.

$$x=\frac{-\left(-24\right)±\sqrt{576-432}}{2\times 3}$$

Tāpiri 576 ki te -432.

$$x=\frac{-\left(-24\right)±\sqrt{144}}{2\times 3}$$

Tuhia te pūtakerua o te 144.

$$x=\frac{-\left(-24\right)±12}{2\times 3}$$

Ko te tauaro o -24 ko 24.

$$x=\frac{24±12}{2\times 3}$$

Whakareatia 2 ki te 3.

$$x=\frac{24±12}{6}$$

Nā, me whakaoti te whārite x=\frac{24±12}{6} ina he tāpiri te ±. Tāpiri 24 ki te 12.

$$x=\frac{36}{6}$$

Whakawehe 36 ki te 6.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{24±12}{6} ina he tango te ±. Tango 12 mai i 24.

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

Whakawehe 12 ki te 6.

$$x=2$$

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 6 mō te x_{1} me te 2 mō te x_{2}.

$$3x^{2}-24x+36=3\left(x-6\right)\left(x-2\right)$$

Aromātai

$$3\left(x-6\right)\left(x-2\right)$$