Whakaoti i te p^2+2p-3

$$p ^ { 2 } + 2 p - 3$$

Tauwehe

$$\left(p-1\right)\left(p+3\right)$$

Ngā Upane Otinga

Whakatauwehea te kīanga mā te whakarōpū. Tuatahi, me tuhi anō te kīanga hei p^{2}+ap+bp-3. Hei kimi a me b, whakaritea tētahi pūnaha kia whakaoti.

$$a+b=2 ab=1\left(-3\right)=-3$$

I te mea kua tōraro te ab, he tauaro ngā tohu o a me b. I te mea kua tōrunga te a+b, he nui ake te uara pū o te tau tōrunga i tō te tōraro. Ko te takirua anake pērā ko te otinga pūnaha.

$$a=-1 b=3$$

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

$$\left(p^{2}-p\right)+\left(3p-3\right)$$

Tauwehea te p i te tuatahi me te 3 i te rōpū tuarua.

$$p\left(p-1\right)+3\left(p-1\right)$$

Whakatauwehea atu te kīanga pātahi p-1 mā te whakamahi i te āhuatanga tātai tohatoha.

$$\left(p-1\right)\left(p+3\right)$$

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.

$$p^{2}+2p-3=0$$

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.

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

Pūrua 2.

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

Whakareatia -4 ki te -3.

$$p=\frac{-2±\sqrt{4+12}}{2}$$

Tāpiri 4 ki te 12.

$$p=\frac{-2±\sqrt{16}}{2}$$

Tuhia te pūtakerua o te 16.

$$p=\frac{-2±4}{2}$$

Nā, me whakaoti te whārite p=\frac{-2±4}{2} ina he tāpiri te ±. Tāpiri -2 ki te 4.

$$p=\frac{2}{2}$$

Whakawehe 2 ki te 2.

$$p=1$$

Nā, me whakaoti te whārite p=\frac{-2±4}{2} ina he tango te ±. Tango 4 mai i -2.

$$p=-\frac{6}{2}$$

Whakawehe -6 ki te 2.

$$p=-3$$

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 1 mō te x_{1} me te -3 mō te x_{2}.

$$p^{2}+2p-3=\left(p-1\right)\left(p-\left(-3\right)\right)$$

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

$$p^{2}+2p-3=\left(p-1\right)\left(p+3\right)$$

Aromātai

$$\left(p-1\right)\left(p+3\right)$$