Whakaoti i te 2x^2+16x+24

$$2 x ^ { 2 } + 16 x + 24$$

Tauwehe

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

Ngā Upane Otinga

Tauwehea te 2.

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

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 tōrunga te a+b, he tōrunga 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.

$$a=2 b=6$$

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

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

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

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

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

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

Me tuhi anō te kīanga whakatauwehe katoa.

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

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.

$$2x^{2}+16x+24=0$$

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.

$$x=\frac{-16±\sqrt{16^{2}-4\times 2\times 24}}{2\times 2}$$

Pūrua 16.

$$x=\frac{-16±\sqrt{256-4\times 2\times 24}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-16±\sqrt{256-8\times 24}}{2\times 2}$$

Whakareatia -8 ki te 24.

$$x=\frac{-16±\sqrt{256-192}}{2\times 2}$$

Tāpiri 256 ki te -192.

$$x=\frac{-16±\sqrt{64}}{2\times 2}$$

Tuhia te pūtakerua o te 64.

$$x=\frac{-16±8}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-16±8}{4}$$

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

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

Whakawehe -8 ki te 4.

$$x=-2$$

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

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

Whakawehe -24 ki te 4.

$$x=-6$$

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 -6 mō te x_{2}.

$$2x^{2}+16x+24=2\left(x-\left(-2\right)\right)\left(x-\left(-6\right)\right)$$

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

$$2x^{2}+16x+24=2\left(x+2\right)\left(x+6\right)$$

Aromātai

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