Whakaoti i te 2n^2+28n+96

$$2 n ^ { 2 } + 28 n + 96$$

Tauwehe

$$2\left(n+6\right)\left(n+8\right)$$

Ngā Upane Otinga

Tauwehea te 2.

$$2\left(n^{2}+14n+48\right)$$

Whakaarohia te n^{2}+14n+48. Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei n^{2}+an+bn+48. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=14 ab=1\times 48=48$$

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 48.

$$1,48 2,24 3,16 4,12 6,8$$

Tātaihia te tapeke mō ia takirua.

$$1+48=49 2+24=26 3+16=19 4+12=16 6+8=14$$

Ko te otinga te takirua ka hoatu i te tapeke 14.

$$a=6 b=8$$

Tuhia anō te n^{2}+14n+48 hei \left(n^{2}+6n\right)+\left(8n+48\right).

$$\left(n^{2}+6n\right)+\left(8n+48\right)$$

Tauwehea te n i te tuatahi me te 8 i te rōpū tuarua.

$$n\left(n+6\right)+8\left(n+6\right)$$

Whakatauwehea atu te kīanga pātahi n+6 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(n+6\right)\left(n+8\right)$$

Me tuhi anō te kīanga whakatauwehe katoa.

$$2\left(n+6\right)\left(n+8\right)$$

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.

$$2n^{2}+28n+96=0$$

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.

$$n=\frac{-28±\sqrt{28^{2}-4\times 2\times 96}}{2\times 2}$$

Pūrua 28.

$$n=\frac{-28±\sqrt{784-4\times 2\times 96}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$n=\frac{-28±\sqrt{784-8\times 96}}{2\times 2}$$

Whakareatia -8 ki te 96.

$$n=\frac{-28±\sqrt{784-768}}{2\times 2}$$

Tāpiri 784 ki te -768.

$$n=\frac{-28±\sqrt{16}}{2\times 2}$$

Tuhia te pūtakerua o te 16.

$$n=\frac{-28±4}{2\times 2}$$

Whakareatia 2 ki te 2.

$$n=\frac{-28±4}{4}$$

Nā, me whakaoti te whārite n=\frac{-28±4}{4} ina he tāpiri te ±. Tāpiri -28 ki te 4.

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

Whakawehe -24 ki te 4.

$$n=-6$$

Nā, me whakaoti te whārite n=\frac{-28±4}{4} ina he tango te ±. Tango 4 mai i -28.

$$n=-\frac{32}{4}$$

Whakawehe -32 ki te 4.

$$n=-8$$

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 -8 mō te x_{2}.

$$2n^{2}+28n+96=2\left(n-\left(-6\right)\right)\left(n-\left(-8\right)\right)$$

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

$$2n^{2}+28n+96=2\left(n+6\right)\left(n+8\right)$$

Aromātai

$$2\left(n+6\right)\left(n+8\right)$$