Whakaoti i te 2m^2-3m-9

$$2 m ^ { 2 } - 3 m - 9$$

Tauwehe

$$\left(m-3\right)\left(2m+3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei 2m^{2}+am+bm-9. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=-3 ab=2\left(-9\right)=-18$$

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 -18.

$$1,-18 2,-9 3,-6$$

Tātaihia te tapeke mō ia takirua.

$$1-18=-17 2-9=-7 3-6=-3$$

Ko te otinga te takirua ka hoatu i te tapeke -3.

$$a=-6 b=3$$

Tuhia anō te 2m^{2}-3m-9 hei \left(2m^{2}-6m\right)+\left(3m-9\right).

$$\left(2m^{2}-6m\right)+\left(3m-9\right)$$

Tauwehea te 2m i te tuatahi me te 3 i te rōpū tuarua.

$$2m\left(m-3\right)+3\left(m-3\right)$$

Whakatauwehea atu te kīanga pātahi m-3 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(m-3\right)\left(2m+3\right)$$

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.

$$2m^{2}-3m-9=0$$

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.

$$m=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4\times 2\left(-9\right)}}{2\times 2}$$

Pūrua -3.

$$m=\frac{-\left(-3\right)±\sqrt{9-4\times 2\left(-9\right)}}{2\times 2}$$

Whakareatia -4 ki te 2.

$$m=\frac{-\left(-3\right)±\sqrt{9-8\left(-9\right)}}{2\times 2}$$

Whakareatia -8 ki te -9.

$$m=\frac{-\left(-3\right)±\sqrt{9+72}}{2\times 2}$$

Tāpiri 9 ki te 72.

$$m=\frac{-\left(-3\right)±\sqrt{81}}{2\times 2}$$

Tuhia te pūtakerua o te 81.

$$m=\frac{-\left(-3\right)±9}{2\times 2}$$

Ko te tauaro o -3 ko 3.

$$m=\frac{3±9}{2\times 2}$$

Whakareatia 2 ki te 2.

$$m=\frac{3±9}{4}$$

Nā, me whakaoti te whārite m=\frac{3±9}{4} ina he tāpiri te ±. Tāpiri 3 ki te 9.

$$m=\frac{12}{4}$$

Whakawehe 12 ki te 4.

$$m=3$$

Nā, me whakaoti te whārite m=\frac{3±9}{4} ina he tango te ±. Tango 9 mai i 3.

$$m=-\frac{6}{4}$$

Whakahekea te hautanga \frac{-6}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$m=-\frac{3}{2}$$

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 3 mō te x_{1} me te -\frac{3}{2} mō te x_{2}.

$$2m^{2}-3m-9=2\left(m-3\right)\left(m-\left(-\frac{3}{2}\right)\right)$$

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

$$2m^{2}-3m-9=2\left(m-3\right)\left(m+\frac{3}{2}\right)$$

Tāpiri \frac{3}{2} ki te m mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$2m^{2}-3m-9=2\left(m-3\right)\times \frac{2m+3}{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 2 i roto i te 2 me te 2.

$$2m^{2}-3m-9=\left(m-3\right)\left(2m+3\right)$$

Aromātai

$$\left(m-3\right)\left(2m+3\right)$$