Whakaoti i te 2x^2-8x-24=

$$2 x ^ { 2 } - 8 x - 24 =$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(x^{2}-4x-12\right)$$

Whakaarohia te x^{2}-4x-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.

$$a+b=-4 ab=1\left(-12\right)=-12$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōraro te a+b, he nui ake te uara pū o te tau tōraro i tō te tōrunga. 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.

$$a=-6 b=2$$

Tuhia anō te x^{2}-4x-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.

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

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.

$$2x^{2}-8x-24=0$$

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.

$$x=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}-4\times 2\left(-24\right)}}{2\times 2}$$

Pūrua -8.

$$x=\frac{-\left(-8\right)±\sqrt{64-4\times 2\left(-24\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-\left(-8\right)±\sqrt{64-8\left(-24\right)}}{2\times 2}$$

Whakareatia -8 ki te -24.

$$x=\frac{-\left(-8\right)±\sqrt{64+192}}{2\times 2}$$

Tāpiri 64 ki te 192.

$$x=\frac{-\left(-8\right)±\sqrt{256}}{2\times 2}$$

Tuhia te pūtakerua o te 256.

$$x=\frac{-\left(-8\right)±16}{2\times 2}$$

Ko te tauaro o -8 ko 8.

$$x=\frac{8±16}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{8±16}{4}$$

Nā, me whakaoti te whārite x=\frac{8±16}{4} ina he tāpiri te ±. Tāpiri 8 ki te 16.

$$x=\frac{24}{4}$$

Whakawehe 24 ki te 4.

$$x=6$$

Nā, me whakaoti te whārite x=\frac{8±16}{4} ina he tango te ±. Tango 16 mai i 8.

$$x=-\frac{8}{4}$$

Whakawehe -8 ki te 4.

$$x=-2$$

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}.

$$2x^{2}-8x-24=2\left(x-6\right)\left(x-\left(-2\right)\right)$$

Whakamāmātia ngā kīanga katoa o te āhua p-\left(-q\right) ki te p+q.

$$2x^{2}-8x-24=2\left(x-6\right)\left(x+2\right)$$

Aromātai

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