Whakaoti i te 2x^2+20x+48

$$2 x ^ { 2 } + 20 x + 48$$

Tauwehe

$$2\left(x+4\right)\left(x+6\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(x^{2}+10x+24\right)$$

Whakaarohia te x^{2}+10x+24. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei x^{2}+ax+bx+24. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=10 ab=1\times 24=24$$

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 24.

$$1,24 2,12 3,8 4,6$$

Tātaihia te tapeke mō ia takirua.

$$1+24=25 2+12=14 3+8=11 4+6=10$$

Ko te otinga te takirua ka hoatu i te tapeke 10.

$$a=4 b=6$$

Tuhia anō te x^{2}+10x+24 hei \left(x^{2}+4x\right)+\left(6x+24\right).

$$\left(x^{2}+4x\right)+\left(6x+24\right)$$

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

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

Whakatauwehea atu te kīanga pātahi x+4 mā te whakamahi i te āhuatanga tātai tohatoha.

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

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(x+4\right)\left(x+6\right)$$

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.

$$2x^{2}+20x+48=0$$

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.

$$x=\frac{-20±\sqrt{20^{2}-4\times 2\times 48}}{2\times 2}$$

Pūrua 20.

$$x=\frac{-20±\sqrt{400-4\times 2\times 48}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$x=\frac{-20±\sqrt{400-8\times 48}}{2\times 2}$$

Whakareatia -8 ki te 48.

$$x=\frac{-20±\sqrt{400-384}}{2\times 2}$$

Tāpiri 400 ki te -384.

$$x=\frac{-20±\sqrt{16}}{2\times 2}$$

Tuhia te pūtakerua o te 16.

$$x=\frac{-20±4}{2\times 2}$$

Whakareatia 2 ki te 2.

$$x=\frac{-20±4}{4}$$

Nā, me whakaoti te whārite x=\frac{-20±4}{4} ina he tāpiri te ±. Tāpiri -20 ki te 4.

$$x=-\frac{16}{4}$$

Whakawehe -16 ki te 4.

$$x=-4$$

Nā, me whakaoti te whārite x=\frac{-20±4}{4} ina he tango te ±. Tango 4 mai i -20.

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

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 -4 mō te x_{1} me te -6 mō te x_{2}.

$$2x^{2}+20x+48=2\left(x-\left(-4\right)\right)\left(x-\left(-6\right)\right)$$

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

$$2x^{2}+20x+48=2\left(x+4\right)\left(x+6\right)$$

Aromātai

$$2\left(x+4\right)\left(x+6\right)$$